05_theorie_filled.ipynb

{
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  {
   "cell_type": "markdown",
   "id": "dd6e07d1",
   "metadata": {},
   "source": [
    "# Schleifen und Rekursion\n",
    "\n",
    "#### Patrick Schnider, Marcel Lüthi</br>Departement Mathematik und Informatik, Universität Basel"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "42f08f48",
   "metadata": {},
   "source": [
    "In diesem Notebook brauchen wir erneut Turtlegrafik.\n",
    "Führen Sie bitte die folgenden zwei Zeilen aus, damit Sie die Turtlegrafik-Kommandos zur Verfügung haben."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "3e086a64",
   "metadata": {},
   "outputs": [],
   "source": [
    "%mavenRepo shapemodelling-repo https://shapemodelling.cs.unibas.ch/repo/\n",
    "%maven ch.unibas.informatik:jturtle:0.7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "033713da",
   "metadata": {},
   "outputs": [],
   "source": [
    "import static ch.unibas.informatik.jturtle.TurtleCommands.*;\n",
    "import java.awt.Color;"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8b422fb6",
   "metadata": {},
   "source": [
    "### Teil 1: Schleifen\n",
    "\n",
    "In dieser Woche haben wir Schleifen als Alternative zu Rekursion kennengelernt. \n",
    "Im ersten Teil dieses Notebooks werden wir die verschiedenen Varianten von Schleifen anschauen und diskutieren, welche Schleifenart wir für welche Anwendung einsetzen. Zuerst greifen wir auf die Aufgabe von letzter Woche zurück, nämlich das Zeichnen eines n-Ecks.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "32b32000",
   "metadata": {},
   "outputs": [
    {
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      "text/plain": [
       "BufferedImage@3b608314: type = 2 DirectColorModel: rmask=ff0000 gmask=ff00 bmask=ff amask=ff000000 IntegerInterleavedRaster: width = 1024 height = 1024 #Bands = 4 xOff = 0 yOff = 0 dataOffset[0] 0"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "class Drawing {\n",
    "    \n",
    "    // Rekursive Lösung von letzter Woche\n",
    "    public static void drawPolygon(int n, int length) {\n",
    "       drawSideAndTurn(n, 360.0 / n, length);\n",
    "    }\n",
    "    \n",
    "    // Hilfsmethode für die rekursive Lösung von letzter Woche\n",
    "    public static void drawSideAndTurn(int n, double angle, double length) {\n",
    "        if (n == 0) {\n",
    "            // do nothing\n",
    "        } else {\n",
    "            forward(length);\n",
    "            turnLeft(angle);\n",
    "            drawSideAndTurn(n -1, angle, length);\n",
    "        }\n",
    "    }\n",
    "    \n",
    "    public static void drawPolygonForLoop(int n, double length) {\n",
    "        \n",
    "        for (int i = 0; i < n; i = i + 1) {\n",
    "            forward(length);\n",
    "            turnLeft(360.0/n);\n",
    "        }\n",
    "    }\n",
    "\n",
    "    public static void drawPolygonWhileLoop(int n, double length) {\n",
    "        int i = 0;\n",
    "        while (i < n) {\n",
    "            forward(length);\n",
    "            turnLeft(360.0 / n);\n",
    "            i = i + 1;\n",
    "        }\n",
    "    }\n",
    "\n",
    "    public static void drawPolygonDoWhileLoop(int n, double length) {\n",
    "        int i = 0;\n",
    "        do {\n",
    "            forward(length);\n",
    "            turnLeft(360.0 / n);\n",
    "            i = i + 1;\n",
    "        } while (i < n);\n",
    "    }\n",
    "\n",
    "    \n",
    "    public static void main(String[] args) {\n",
    "        home();\n",
    "        reset();\n",
    "        clear();\n",
    "        penDown();\n",
    "        drawPolygon(5, 10);\n",
    "        display(drawing());\n",
    "    }\n",
    "}\n",
    "\n",
    "Drawing.main(new String[0]);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fc5ce8ac",
   "metadata": {},
   "source": [
    "#### Miniübungen\n",
    "\n",
    "* Implementieren Sie die Funktionalität zum Zeichnen eines n-Ecks, indem Sie einmal eine `for`-Schleife, einmal eine `while`-Schleife und einmal eine `do-while`-Schleife nutzen.\n",
    "* Welche Lösung würden Sie bevorzugen?\n",
    "* Sind alle Lösungen korrekt?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "00b387da",
   "metadata": {},
   "source": [
    "#### Spirale\n",
    "\n",
    "Als nächstes möchten wir eine Spirale zeichnen. Dies machen wir, indem wir uns in einer Schleife jeweils um denselben Winkel drehen und dann ein Stück vorwärts gehen. Das Stück, welches wir vorwärts gehen, wird in jedem Schritt etwas grösser. Wir beginnen mit einer initialen Schrittlänge, und brechen ab, wenn wir eine gewisse Schrittlänge erreicht haben. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "7f3e753f",
   "metadata": {},
   "outputs": [
    {
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",
      "text/plain": [
       "BufferedImage@86567ff: type = 2 DirectColorModel: rmask=ff0000 gmask=ff00 bmask=ff amask=ff000000 IntegerInterleavedRaster: width = 1024 height = 1024 #Bands = 4 xOff = 0 yOff = 0 dataOffset[0] 0"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "class Drawing {\n",
    "    \n",
    "    public static void drawSpiral(double initialLength, double finalLength) {\n",
    "        penDown();\n",
    "       \n",
    "        double length = initialLength;\n",
    "        while (length < finalLength) {\n",
    "            forward(length);\n",
    "            turnLeft(50);\n",
    "            length = length + 1;\n",
    "        }\n",
    "    }\n",
    "    \n",
    "   \n",
    "    public static void drawSpiralRec(double currentLength, double finalLength) {\n",
    "        penDown();\n",
    "       \n",
    "        if (currentLength >= finalLength) {\n",
    "            return;\n",
    "        } else {\n",
    "        \n",
    "            forward(currentLength);\n",
    "            turnLeft(50);\n",
    "            drawSpiralRec(currentLength + 1, finalLength);\n",
    "        }\n",
    "    }\n",
    "    \n",
    "    public static void main(String[] args) {\n",
    "        home();\n",
    "        reset();\n",
    "        penSize(1);\n",
    "        clear();\n",
    "        penDown();\n",
    "        \n",
    "        drawSpiralRec(1, 50);\n",
    "        display(drawing());\n",
    "    }\n",
    "}\n",
    "\n",
    "Drawing.main(new String[0]);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "be35c90f",
   "metadata": {},
   "source": [
    "#### Miniübung \n",
    "\n",
    "* Welche Schleife nehmen Sie hier bevorzugt?\n",
    "* Implementieren Sie die Methode `drawSpiral`.\n",
    "* Für ganz Schnelle: Können Sie die Methode auch rekursiv schreiben?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "55d872a6",
   "metadata": {},
   "source": [
    "### Eingabe mittels Scanner"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5dda90db",
   "metadata": {},
   "source": [
    "Zum Schluss zeigen wir noch ein Beispiel, bei dem die do-While Schleife die bevorzugte Wahl ist. \n",
    "Diese Schleife ist immer dann nützlich, wenn wir eine Aktion mindestens einmal durchführen müssen, bevor wir Entscheiden können, ob ein weiterer Durchlauf gemacht werden soll. Das typische Beispiel dafür ist das Lesen von Daten aus einer Datei oder der Tastatur. Dies wird in folgendem Beispiel gezeigt:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "1cdfdd04",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Enter your name\n"
     ]
    },
    {
     "name": "stdin",
     "output_type": "stream",
     "text": [
      " \n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Enter your name\n"
     ]
    },
    {
     "name": "stdin",
     "output_type": "stream",
     "text": [
      " \n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Enter your name\n"
     ]
    },
    {
     "name": "stdin",
     "output_type": "stream",
     "text": [
      " Hi\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Username is: Hi\n"
     ]
    }
   ],
   "source": [
    "import java.util.Scanner;  // Import the Scanner class\n",
    "\n",
    "class Input {\n",
    "    \n",
    "    public static String askForUsername() {\n",
    "        Scanner myObj = new Scanner(System.in);  // Create a Scanner object\n",
    "        System.out.println(\"Enter your name\");\n",
    "        String input = myObj.nextLine(); // programm stops until the key [Enter] is pressed\n",
    "        return input;\n",
    "    }\n",
    "\n",
    "    public static void main(String[] args) {\n",
    "        String userName;\n",
    "        do {\n",
    "            userName = askForUsername();\n",
    "        } while (userName.equals(\"\"));\n",
    "        System.out.println(\"Username is: \" + userName);\n",
    "    }\n",
    "}\n",
    "\n",
    "Input.main(new String[0]);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5d0d08ec",
   "metadata": {},
   "source": [
    "#### Miniübung \n",
    "\n",
    "* Schreiben Sie dieses Beispiel so um, dass eine while-Schleife verwendet wird. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "5f13fce8-d955-46f8-a333-e43cdc2e6a00",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Enter your name\n"
     ]
    },
    {
     "name": "stdin",
     "output_type": "stream",
     "text": [
      " Test\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Username is: Test\n"
     ]
    }
   ],
   "source": [
    "import java.util.Scanner;  // Import the Scanner class\n",
    "\n",
    "class Input {\n",
    "    \n",
    "    public static String askForUsername() {\n",
    "        Scanner myObj = new Scanner(System.in);  // Create a Scanner object\n",
    "        System.out.println(\"Enter your name\");\n",
    "        String input = myObj.nextLine(); // programm stops until the key [Enter] is pressed\n",
    "        return input;\n",
    "    }\n",
    "\n",
    "    public static void main(String[] args) {\n",
    "        String userName = \"\";\n",
    "        while (userName.equals(\"\")) {\n",
    "            userName = askForUsername();\n",
    "        };\n",
    "        System.out.println(\"Username is: \" + userName);  // Output user input\n",
    "    }\n",
    "}\n",
    "\n",
    "Input.main(new String[0]);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dde8b4e7",
   "metadata": {},
   "source": [
    "### Teil 2: Rekursion\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e8b84735",
   "metadata": {},
   "source": [
    "Angenommen Sie wollen eine Methode schreiben, die die Zahlen von $m$ bis $n$ aufsummiert und das Resultat zurückgibt. Mit einer `for`-Schleife ist diese Aufgabe sehr einfach zu lösen (siehe Methode `sumNumbers` in Zelle unten). Dasselbe können wir aber auch mittels Rekursion machen. Der Schlüssel zur Lösung gibt die folgende Einsicht\n",
    "\n",
    "- Die Summe der Zahlen von $m$ bis $n$ ist gleich $m$ plus der Summe von $m+1$ bis $n$, oder in Formeln\n",
    "$ \\sum_{i=m}^n i = m + \\sum_{i=m+1}^n i$\n",
    "\n",
    "#### Miniübung\n",
    "\n",
    "* Was wäre das Abbruchkriterium für die Rekursion?\n",
    "* Implementieren Sie diese Strategie."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "f8739755",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sum of the numbers 0 to 100: 5050\n"
     ]
    }
   ],
   "source": [
    "class SumExample {\n",
    "\n",
    "    public static int sumNumbersLoop(int from, int to) {\n",
    "        int sum = 0;\n",
    "        for (int i = from; i <= to; i = i + 1) {\n",
    "            sum = sum + i;\n",
    "        }\n",
    "        return sum;\n",
    "    }\n",
    "\n",
    "    public static int sumNumbersRec(int from, int to) {\n",
    "        if (from > to) {\n",
    "            return 0;\n",
    "        }\n",
    "        return from + sumNumbersRec(from + 1, to);\n",
    "    }\n",
    "\n",
    "\n",
    "    public static void main(String[] args) {\n",
    "        int sum = sumNumbersRec(0, 100);\n",
    "        System.out.println(\"sum of the numbers 0 to 100: \" +sum);\n",
    "    }\n",
    "}\n",
    "SumExample.main(new String[0]);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8fbea15c",
   "metadata": {},
   "source": [
    "### Die Ästhetik der Informatik"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "baf44624",
   "metadata": {},
   "source": [
    "Inzwischen können Sie auch schon die Zeichnung des Baums verstehen, welche wir Ihnen am Anfang der Vorlesung gezeigt haben. Diese nutzt einfach die Idee, dass ein Baum wieder aus kleinen Teilbäumen besteht. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "57fe37dd",
   "metadata": {},
   "outputs": [
    {
     "data": {
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dejG9eQDget7GAD9g18dTlicbK/Xmdzv70XzG7tpn88W18f6sMl8td2281HvO1hwAcB9vZIAfsPMDKsuVjZV68zsdH5N31jzsrLsrV5ljR77SSO7aeKn3rK05AOA+3sgAP2D3B1SWr/URVxu/wtHHnTVLu2rvyvNx5NmV71Dmy3JnY5nWs9bGZ7RytOYAgH/z1gT4Abs/clr5srls7CrHx+SdNUu7au/Kc9id7yPmK+/jXEutt2xsVi33R20cAMh5cwL8gCs+dFo541y8v9Lxwbez5kyuHbV35Iiuypndx/Ge7O9sNkdNzFuqjQMAOW9OgEWtD5PdrqrTyls+Xytup/JDcufvO5NnR91ejtZcTS/nijLfmd/8WBP/e1YrXzYGALR5ewKctPrRNOOq/CN573i+Q1lrZ93ZPGdr99aXzzijl3dWmetM7vg8q3miVr5sDABo8/YE2OTMB1TPVXk/ermP5+rF7VDW2VlzNs+Z2iNry/lebGkk94zYx5ncx/ozOUqxt1K8BwDGeIMCbLbzI6h0Rc5DL/dVzxSVdXbWnM1zpnZvbTaXjWV6uWft/K135CiVuWLeeA8AjPEGBbjIlR9Eu43k3v08mbLGznoreVbr99bV5mrjUS//qDLHjpw7chxintgrALDGWxTgYrs+jHbkaOnlP56jF3dGzB/vV63kWKk9sqY135o7jNQYsft33pHjkOXZmR8A3sqbFOAmZz9gzqwd1atx9hl6Yv54v2olx0rtkTWt+dbcYaTGiCPHjnxHjrN5Pmo5zuY/ux4A/gJvQoCbrX6IrKxZ0auz2v+ImHvXh+XK+pW6I2vOzn+M1Ok51u/KdTbHRytHa66l7G01BwD8Fd6EAF8SP0x2XWf18uysVcpy7qq1un6m9kivrblSL65XZ8RIv6N25qlpzWWynuI9ALyNNyHAl2UfKpnRmN1XpjW3qpaz18uI1bUzdUdie/OlVuxIrZ4dv+thR57W+tn8WWw2BgBv420I8BC9j5zW3G7lx2Gtr9r4qlq+Vg+jVtfO1B2J7c1HrfiRei07ftfDjjyt9aP5W3G1cQB4E29DgId50kdM+ZEY+8rGzqjlKsez+RFn1tX6Ks3EzaqtGanXcnb9YfTZW1prj7leTGv+ozefWVkDAE/mzQbwUNlHTby/S/mRV/aV9biqliuOZzE9K2sOsX5mJOZjJCaTrRutWXN2/eHIcyZXa+0xV4upjUejcYfZeAD4Bd5uwJ/z1zbu5cfVt5+t/Ngre9rRVy1PHM9ielbWHGL9zGjMGXH9UTOOj1hdlznTx0drXTkX42ZrXhULAL/EGw74k2Y/Dn7B2Q+tncpedvXVyhHnanE1s/GlWDszGnNGtn6kbmZ1XebItZKvtS6Ol/dxbsTomtE4APhF3nLAn/bXNvOtD6ZvKD/+zvbVyhHnanE1s/FRrF9qzZVGYnpijtHa0eq6qMyzkrMVH+eO/HF8xOia0TgA+FXedMCft/rR8FRPfJ7y42y1t9babC7et8zEZrL6h9ZcaSRmRJln5TdfWVMT88zkbPURx2pxo0bWnq0BAL/Amw54jb+yuW99OH1T2ddsf734bD7e14zGtWT1D6250kjMqDJXVj/el474VsyomGcm5xGbrclyZnGjRtaOxIzYlQcAruAtBbxK/GD5VU99jqOvePWMxGUx8T4zEtNTe5ZsLDMSM+vIWfbQ66d8jlbcqJhnNGeMy3Ks5s701vbmZ+zMBQC7eUsBrxQ/Ln7RU5+h7Ov4c6/X3vxHFpONRb35UVmtbCwzErMi/r69OmVML7YnqzmaM8aVPcWch9r4iNa61tysnbkA4AreVMCr/fKGvfWx9E1ZX+VY1m9tvFSLycZKvflRWf1sLDMSs6r1u0Zl3Eh8S1Yz3meymNFn6M1nWmtacyt25wOA3bypgNcb+fB4qqf2nvVVfuTF+XifacXUxj9aczNi/XjfMho3q/Z7ZmJML74n5jvGemLMaP8fIzFRbU1tfNXufABwBW8rgP/5xQ38zMfT3Wp9lT3Hq6UVl40dWnOzyvq1XjKjcTNme4kxvfiemO8Ya4nzR47yOVp685lsTTZ21hU5AWA3byuAQvZR83TxI+open2V8624UitudnxFWb/VSzQaNyrL1+on+41rsaNivmOsJdaPOWbWj4pr4v0OV+QEgCt4YwEkfm1DHz+kniL7yIvKmFbcRytmdnzFTK+H0bgRrbqzc/F+RpbvGK8p51q/YTZ2aM3VxLpXuCovAOzmjQV83VM3z7UPlCdqfVB9W6+vsvfec7TmPrK5bGzVSI/RaFxPr2arrziexcyI+crxmmOu1edHbfyjNVdT1r3KlbkBYCdvLODrnr55fnp/h9ZH1TeNfPCVc2V8XJONlbK5bOyMWm81o3Etozmy3uL9MXZGlvMYzxzjWX/R6lwm1r3CVXkB4AreWsDX/cIG+soPiJ2e2mfrw683HufjfRTn4v1ZWU8to3GZmTofZXz535gj3s/Kch7jUfl71dZFtZjaeE38La5wZW4A2M1bC/i6X9pAP73XmY+su9X6qo0fymcafb5yvhc7a7SHw2hcNFPjENfUeo33M7J8h2y81kNLLbY2XjNbd9aVuQHgCt5cwNf92ib66o+Ks57aX+1DMBvLlOt7a8q5VtyKkfqHkZjM6rqPsrdan9nYqFrOQ/zte/E12ZpsrGU2ftbV+QFgN28u4BF+cSO9+mFzh6f2ln0QxvueLEfmmO/FzRqt/zESUxrN21LmqPUa72dk+Uq92qOyddlYzZnaI67MDQBX8fYCHmHXZrr86Lj6A+BwR41Zdz7/rNhXvO8Z/fs95loxK0ZqH0ZiDqM5e7LfJ+aN9zN6fWb1V8X18b5mV/2WK3MDwFW8vYBHuHIzHT9IsuusXXl2emJPh7K3lT5H//568ytG6h5GYj5G40ZlPdb+PCPLG43EjIo54n3miBmJPePq/ABwBW8v4BG+vZkuP1qya9RM7B1m+79L/H1XehxZ35pb1atZ6sWM5plV6/G4j+OjspylWt0zyly9vDOxZ1yZGwCu5A0GPMLTN9Tlh03tymJnzMaPWO3lDjt6q/0dxPmdWvVKI/O9mFWtHmvjI1pry5q1mBUxV7w/xPF4v9OVuQHgSt5gwCP8hQ11/ACKV89IzIrR+t8w8/vUtHK05laN5mzNt+Z2aPVYGx+RrS1rZfNnxZxZ/tGxHX4tLwCUvG2AR/irm9/4YRQ/ZqLW3Bm9ut8y8pv09H7b2viqVq1SNj+y7qyR/nrzNXFdrBXnd4k1S7Wa2dgOv5YXAEreNsAjvGHzW34sxauMuUJW6wl29VX7Pcu5XWp1ojg/smaHkf5685m4JqsT73eJNUrxvja2wx3Pl+nNA8AobxTgEd62wS0/nuJ1lavzr9j53LXfMd6fldXIxB7uMtJfbz5TrslqxPvdytpxLKqNn3V33qt/UwDex1sFeIy3bnTLj6l47XZV3lW7nzX7/Xbm/4j5M1fVHjHaX2s+U+bN1mdjO5W/afnfTGvujLvyXv1bAvBe3i7AY9jw5h9ZOz8Gduc764p+spzx/owsfzQSc5WR2r35TJk3W1sb36lVv9SbX3FFzo8y78izAcAZ3jLAY9j4/lf2QRCvM3bk2GXXM5Wy32pnjZg7as3dodffYSTmkP2mUWtul9EaIzGzrsj50ftdAWAnbxvgMWyA/6v2O8SPsDMfDWfW7nb2WaL4+1yZP2rN3WW0h5GYj5HfsDW302idkZgZu/MdRp8HAHbx1gEe400b4d6zjsxn16iVNVfZ3cuRJ/42O/PX8tXG79TqrzQT04vtze8yUqc3v2J3zpHfFACu4M0DdN21Sb2rzhP0nrU3Xyo/JuLVMhJzh9F+R8QcM7/HqFq+2vjdRvuYiRmNu1JZo1WrNbdqV874O+3KCwCjvHmAIXdsVO+o8RS9Z+3N1xwfGNmVac3dpdfjjCzHyO8wo5YrG7tbrbeaVuzM7zYSc1ZZo1WrNbdiR77a75ONAcCVvHmAYVdvVq/O/zSt523NjTo+OrIriznjzPqVHrLYbOyj9uyrslzZ2DfM9lGLnfnNRmJ2KOu06rXmVpzJ1/ptauMAcCVvH2BKa0N71pW5n6j3rL35Gcdv27vOWF2/Uj+LzcYOu58z5on335L11lKLnckzGndG1k+tZm18xZlcvbW9eQC4grcPsOSqzetVeb+l9TytuY/e/BnlB1W8Vh1rZ3Os1I6x8T6z8znLHGfz7RR768liZ3+n0bgzshrxvjZ2xkq+rNfMSAwA7ObtAyy7YgN7Rc5vaj1Pa+6jN7/L8cFSXqtG1mYxs7Vj7Mi6+IwjazJx/Zlcu8XeemL8yu8zE7uqViOOxfszZnPVesyMxgHAbt5AwCm7N7K7831b63lac4eRmB2Oj5fyWjG6NsbM1i1jR9d87HzGs3musNJTfJaZ9TOxZ9TqxLF4f8ZorlpvLbPxALCLNxBw2s7N7M5cT9B6npEPh978Tkc/5TXjiB9dV8bN1ixjR9d8xOebWXuI61dyXGWlp/gs2dps7KMWv1OvRjnXipvVy9Xrq2V1HQCc5Q0EbLFrQ7srz9VG++zFnZ0vzcRmjvXHh83sB04ZO7Iuxs/Um40/xGfbkaMc/7asr574PNnabOyjFr9Tr8YVfwetPL1+es6sBYCzvIWAbc5ujD/Orr/TyPNePX8Yjes58hzPNvKMHzEm3tdk9UbMxh/KNbPPeKitm8lxhaynEbXnKedramt2GqlxzPfiRmV5RvoYsSMHAKzyFgK2O7PBPbP2W1o9t+Y+evMfu2JGlHmOD57yqsnmsrHMaI3SbPwhrtlZO97frdZXy8jzt8ZrczuN1BmJGRXz7Mz9sTMXAMzyFgIusbrJXV33bbWPhGys1Jv/6MX05mfEXMdzlVeUjR1ac6VW/sxsfCmum81Vi4/3d6v11VKuqa1rjdfmdhmtMRo34sizM2fpipwAMMpbCLjM6kZ3dd0TlL2PPMfZmNbciizf8SFUXnG+pjVXauXPHDEjsVGssVI7i433d6v1VROfu7auNV6b22W0xmhcT++3OOuqvAAwypsIuNTKhndlzS47as9+RPTiWvOtuRWtfOVzHXGt+MNIzEfM3TJTP8pqZM+WacXF+7vV+srE56ity8YOtTU7jdYYjWvZkaPn6vwA0ONNBFxudtM7G7/brvqjeUbisphs7KxezuMjqbxGjMSN5owxvfhSq8bIc9Vijj/X1t0h6yvTeoa4Nt4fstjdsh5rRuMyM3XOuqMGALR4EwG3mNn4zsReZUcPox8WvfmPGBPvdxnJWz7XSPzHSNxozhjTiy/1arSeLc5lPcQ1d8r6ytTiamOZLHbU6LqZGjOxpdpvcYU7agBAj7cRcJvRjfZIzB3O9lGub+VqzR1iTLzfZTRv+eG06+91NF+cb8WW4praulofcbycj//9hthTJus9zpX3NTF21MyamRozsYfa73CVu+q03Pm8ADyTtwBwu94GtDd/l7N9xPW1zXc2ljniRuNXjOYuP57Kq6UXE/NksdlcFpeJa2rrsmeK8VnMMf4NtX5KvZg4nsUcYuyIlfjRNTOxH63f4Sp31ip941kBeC5vA/gBf3Hj1nqm1tzdzvRSW5ttxuN9Jlu320iNMub4c3m1tOZjjiw2m8viohjT6zU+U4xvjX9D1kup1m8pzvfiZqzEz6yZiY/PeYc7a3184xkB+A3eDPAD/uomrvZctfFvWe2ntS5uzluxh7jmKr0acb782BjpsTafrR/5c3ZfyuZinUzrmVrj31Dr59CbP4zE9eZLM7GllXUja0ae7wpX1yuf6+paAPw2bwn4AX95Q5c9Wzb2bSs9jayZ2bSPxPSM5GjF9OZGnqc3F9cff87GavelbC7WqKk9UzZ2jN9lpJ84l82XRuJ684eRmJrRGqXempFnu8oVNb/5PAD8Lm8N+AF/fYOXPV829m2zPc3Ej8Tu2OyPrG/FtOY+yo+SVmxtrrZ29v5QG//I6kTxeY74eF/G3yHWafVTm8uMxPbmP3rzPSM1otaakee6ys6a33wOAP4GbxD4EXdv+L5Rr6x5d/1RM33NxsbfoHSMt2JGjKytxdTGo/JZWv1m47U1cSybz9TGP2q1DvEZyth4X665UlazHI9ztfGaXnxr7tCb7xmpkamt6z3T1c7W/Xb/APwt3ibwI76x+ftmzW/UHjXa22jcR7nBj+vK+1rMjN7a2nxtPHM8T3lFtbEYH5+5ti7KxkpZrVI5V8bGK665Sit31k+rz5ZWfGvuozU3qlejJlu38vy7rdR+Qt8A/E3eLPAjvrUR/Ebdp298R3sbjTuU8eVvEPOc/X16a7P5bKzn6LO8ojiWxcY/xzWHGNeT1WrNlWPZfBmzWy9n7KfVY09rTW9uh1aNlrhu9fl3mqn9hH4B+Pu8ZeBHfGtT+I26v7ARHultJKaUxbfGsrkRvXXZfDY2ovy7rP2dlmMxrhdfinl6av181Obis9RidhrJF3tq9dfTWleby8ZW7Or7TJ6dWvXLHltxALCTNw78iG9uEL9R+xc2xb3+evNRjI8fM3E8/nlUb02cj/crjmeIz3LMlX8uY2LsMVYbL/87IssVe4jK+SwmG1tRyx/FXuL9jNba1vgutRojyt7P5Nkp9vCk3gB4J28g+BHf3jDeXf9XNsq1/mrjLXFN7b42PqoXX87v/Dso/05jzqxmjDn0foc43pLVycZKrec45s+ayRH7afXWc6zJ1tfGdspqjDr77LvF3/IJPQGAtxH8iCdsHu/u4Vc2zVmP2VhPuaa2PvuYqMXWjMQfMSOxM8r+y+eIzxOfsZStOWRjLbFOvM/E/mN8vJ81uz72kvU06liX5SjHsvkdzuQ9++w7PakXACh5M8GPeMpG8s4+fmkTHXuM96NGnjf7XXprol58VmOXMndZo/xvq3brueN9T6wT7zOx9xgf72esrI29rOQ4HGuzPDvyt5zJfXVvM57SBwBkvKHghzxhU3l3D7+0mS77nOn5iK19xMT7YyyOx/uWXmyWf6fyWcta2VgUx+PaGbFeb32sla3r5cjEHDNqfcyKz5Ddn8nfs5p/1/Pv8IQeAKDFWwp+yFM2lnf28ZSN/Yiyx5l+j9jac9bGsvh4X9OKq+XeraxTuzLZ+DGWzdWUa3o1D6018b+jZuNLsY+zuco/t+6vsFKjXLOyfqdv1weAEd5U8EOetLm8s5df2liXHyMzjmfM1mVjH/Hjp/xvTyuu1csVynrxymTjvTWZI3ZmbbYmrh3Jc5iJzdR6WBHXlzl35O+ZqZE9c7y/U9YPADyRNxX8kKdtLu/q59c21yu9tp4xG/uIa+J/W1oxtT6uVD5LfK4ojsfnjvM1ZXyr3qGcj33GuRGjcaWyVqy/ku+QrY25s5hdZvLX+snG7lDrBwCeyNsKfsgTN5h39fRLG+zVXlvrWuPHXBlTiz+05lt9XOmoG68ojsXnjvM15e82si6rk60dydOLKWU14nicm5Wt35m/Z7RGq5/a+JVa/QDAE3ljwQ954ibzrp5+baO90mtrTWu8XFfG1dYcarGtPq5WPk+tj9hrqbYmU/5mI+vK+OO/tbXx/lAbj2p5D7F2LW5Utn5n/p6RGr1eWnNX6PUDAE/krQU/5Kkbzbv6+qXN9kqvrTW18Y+47vhza81HLS7mu9NRO14xpvxvlK3JlHl6a7KaIz32xg6tXJnZ+JZs/TG2q0bLSI2ZmDuM9AMAT+TNBR0jG7yRmB3uqrPirt5+ZdM922fvg6I2/hHXlrG9deV/y/E4VjMaN6p8lvhcZUz53yhbE5XztTqlbH6kx9r9MZat7Yl1Z9dH5fqYb1eNll7+0R5GYnYY7QcAnsjbCzpGN3ojMTvcVWfFHb2N/n1822yfvY+K2vghrq39uRTX9MZrZmJ7yt8hXjGmpReT5RuNL+9bPZbz5Xgcm1WruarsNdpZp6aVf6b+aNwZM/0AwBN5g8GA0c3eaNwZd9Q4447+fmUDPtNnGZutycaiVo543xrLxntW1mSO+tkV51t6MeVcL2ccr62t9Rjvz4j1dubM7KxTU8s/W3smdsVsPwDwRN5iMGBm0zcat+rq/Gfd0d/M38c3zfRZxtbW1MYPsV7tz8d9HGuNj1hdVzrq964RrdhyvJY3G2/FHHPZ2C67c/fy7KyVqeVeqTsbP2OlHwB4Im8yGDSz8ZuJndXLXW5Ue7FXuaPuN58vk/Uy02OMzdZlY1ErT/bnmDOun7VjbdnD8ed4jWjFluNZ3mzsGI/3tWu3mP9sjZEcu2rVZLlXa66sGbHaDwA8kbcZDJrdAM7EzpjNW25e79zIXl3jrueYEfuZ+b1jXLYmG4t6eWbnV6yuP9bFHo778hpVi6/lz+ayPx/3tesKO2uM5hmNWxVzn6m3uq7lTD8A8ETeaDBhdhM4Gz9iV85yY3vVJnd3vuiKns+K/Yz2mMX17mtirvjneB/nRuu0rOQ41sQeyr7iXE8Wn93Xcpc9Hf+NcXF9zLHLzhqjOXbVqylzn611Zm3mbD+/4q8/HwD/5l99mLCyGVxZ07IzV6bc9MZrxeq6EWf62iXWz+7jWFSLiWPxvibLd9zHufjnOH/GbJ5aj+VYNtcT18T1tbyxnzh/ONPbqJ01RvOMxq0qc++qtSPHx65+fsEbnhGAf/hXHyatbpZW10W78qwoN8WjG+Te/FkjPVwpq132NNJfLSaOZzE12dp4X/73+HOMO2smX9lTXFP2ls23xPi4Nss5U2smtqW1fleNj9Ecu+rVxGfaUWdHnp39PN0bnhGAf/MvP0w6szFcXRftyrNL3MTH3yje73Rl7hG1+vG3yGIOrfn4O46KOeN9HCv/G+POGs3Z6+EYr823ZM9ajmdjx597VvsaXTcaN2Imz0zsrPhMu2qczbW7n6d7y3MC8A//8sOCM5umM2sPO3LcIW7wr+r7ytyHVv7a3DHe6681H8fjfUv2u8f1MSbG79TL2+qh7DP2PCI+YxzPao/mH+1pNC5aXZeZybGrZuaq3GdyXtXTU73lOQH4N//6w4Kzm8Qzaz/Orv+GcnO9u/+r8pZauXtzvf5acx/lXCsuyurG9bG/OL9bK/8xl/URe1zpN66JeeLcqLi+ln9FzLGa52M2x2z8qF3Pk1nNeVU/T/amZwXgH/71h0VnN09n1p9Z+21XbbSvyFlq5W7NfZS9ZX1mY6VyrhWXyXLHfK3erlCr0eoj6zOLa4k5yrGYayVvvHbYmXM2x6660VV5P1byXtnPU73pWQH4N28AWLRjw7i6fnXdU5Qb7l3Psjtf1Mrbq5v1Fv/cWv9xzPfiSmXdWK9Ui7tSrBP7y+bL3yBeo2J8lmMlX7x2iDnP5F3JsbKmZ9fz1MzmvbKXJ3vb8wLwD28AOGHHJmolx8qaJ9q9+d6ZK9PK3Zr7yHqbef4jZiT2UK6J68r7so8Yd6XYQ6nsJettpecsPo71csW6tWuHnTlXcuyqXboiZ2km99W9PNXbnheAf/MWgAlx47Rr8zibYzb+ycpN+Nnn2pWnppW3NfdR62um59G4jzKuVuO4L+djzNXKHuJ47C+bn+k7xmdX1JqPc7W4FTHfmZyr63fULu16npbR3Ff38WRvfGYA/uEtABOyjVM2tmImz0zsr9i1Id+Ro6aVtzX3UXu+cjzORSMxH1lMtrYcG+3hClndrLeo7LkWc8jyjVwtMWZmbc8VuWbtqn/YnS8zkv+OPp7qjc8MwL95E8CEbPO0cyM5k2cm9leUG/PV5zu7vqWVc6Rm1lvvPhvP5g+1uV7tbP4uWd2st6jsuRZzyPJl16hszWquKObZkWvFjvqHXc/T08t/Rw9P9tbnBuAf3gQwKdtAZWOrRnONxv2is5v0M2sP2fpsrDQyH5+t1ms5Fv+cxR96c1muXi93iLVH+yqfoRaX5cquGdmaM/lKu/J8nMmxq4eP3blqWjV29vCL3vrcAPybtwFMyjZRuzeVI7lGYn5ZuVmffdbVdVFcH++jkfkjpvxvbV02l40dauOH7Hcpx+LcnWLtmZ56sdl8HMvWtWRrzuQ7xByreT52rT+T4+PO56nF7Kj/69787AD8w9sAJtU2UbXxVb18vfm/YnXjvrImU+bo5evNf5R9jTxbFpPFZ2OZLFd23S3Wnuknxpbxcbx1jarFr+Yr7chxOJtjdx9n8oyuzersqP/r3vzsAPybNwJMqm2krthgtnLWxv+icgM/+tyz8S1ljla+kXplTC8+1i3XRdlYTcyVXd/Q6qunFh/Hz9Q4tOJXc37EtbPrS2fXf+zs40yemXWxztnaf8Xbnx+Af3gjwKTWRqo1d0aWNxv762Y38zOxPUeeXr6R+TJXrcds7CNbU4utqfWQ5b5Tq6+eGN+6autG9GJbtXrOrI125jiT50yOlXXlmjO1/5K3Pz8A/+atAAtqG6orN5sxb7x/i3JTP/IbjMaNGMk1Mn/ExD+X4n1p9jfIxNrZ/TfEZ5vpI67Lrqg1l+nF9urVxHUza6Oz6w9neznzPLPxh7LWSt2/yG8AQMlbARa0NlStubPK3FfW+QWjHxYjMTN6uXrzH2XvR/zs321cPyvWzu6/If42s33Etb0cIzGHkbjRutHqusyOHB9n+1lZPxsf7fwd/wK/AQCRNwN/xp0bvladq/soc19Z5xeMbvZ78zN6uXrzH7W+431NXD+yJhNzHHnO5Dwr9jPbR1zbW78S2zKT7xDXjK7LnF1fOtPPyvOMxrXM1vzr/A4ARN4M/Dl3bAB7uXvzZx35r67zK3p/5625WSO/fWvuo+y3jI33NWVclmdU7GOllyvUehoR1/bWj8b25kujOQ+z8TU7chzO5ppZPxo3YqbuX+c3ACDj7cCfdtVmsJfviprRHTV+Sfl3nf0utfFZZY5avtr4odbr8efR9fG+ty7T6mUl3w5ZPyPis4zkiXG12NZcNJLvEGN78S1n15fO9DOzdiRm1EzdN/A7AJDxduAVrtgY9nL15s/a/Tx/Re3vOhtbVebJcmZjUewzron3pexZYr5R5br4XHHsTrP143PEqybGZbGtuUwvX2kmtmVHjtKZfKNre/OzRuu+gd8AgBpvCF5n1yaxt35HjZ47aqz4dk/l33HZS7xfFXNk93EsqvVYao1nc718NbV12dhdaj1lytjWlYkxWWw21tLKVYpxrdies+uj1Z5G1vXmV+z6Hf8KvwEANd4QvNqZDePImpGYM1Z7v8MT+op/v7t+ryxHHCvv49wxFvuLWuO9udp8prYmG7tLradSGZPFx/EsV5yLcXF+RK/mYTSuZ0eOaDVnb11t/Kxe3TfxGwDQ4i0B/zO7gRyJm8m34ur8Zzylt/LvdfbvuKa2vhyv/bkcG+kli8nGSqO5D6342viVyn5qtbP5eF+OZXNxvnU/a6ZuLWbU2fWZlb5aa2rjO+z6Hf8KvwEALd4SkBjZTLbmSqNxq3p9ftOT+oofCWd6a6095sr/7rzKnC1xTUtWI87dqdVPnG+NxfHefDYW50b11vfmR+3IkZnN23qeeL9bre4b+Q0A6PGmgIbexrI2Xmqt3+Hq/Gc9qbfy73Pkd4uxZ66oNZeJ+UbWzcZl8bXxK8V+jtrZWFyTGVlXjrfiR7VyxLk4P+Ps+prZ3rL4eH+VrPZb+Q0A6PGmgEHZJnN0szUatyL29ERP6q/8e1zta2RdmT+LX+0h9t9bPxNTi62NXyX2k121+ExcW8ZlY63xUbV6vbkZO3LUzOTOnmdk3Q5Z7bd6yvP7OwF4Nv8yw4LZzc1M7Iqr85/1tP7OblBH1rRqtOZ64tp4ZVpzH70ctfErlLViX7U+auOlmCOrUYtfEWtl9c7k/zi7vmWmvxg7smaXWPvN7voNyt88uwB4Nv9SwwkzG5/e/Bkj9b9td39n88383WVG1mT5jz9ncyOyNfFZ4nwZk+mt/WjN7VTWiX1l9VtzpZgnq1GLX9WrtyP3VUZ7jM/Ti9/pW3WfaOfzx981XgD8Nv+SwwlxM9TaJNXGd2jVfZKd/e3IdWZjOxpf5i7XnKkb15T54xXj4lg5XltXxlwt9tHq6aM1F8V88arFror5s2vV2fU9rR7jM2TXHe6u92Qzv0H8u4oXAH+bf+nhpGzDVNtMxfudsnpPtKvHnXlqf18to7G1/NnYiLimtj7WPeLi+lZsLeZKsY941WJHxXy1HLXxGTF/vFadXT8i9jpyjazf6aq8vyY+f/zN4wXAu3kTwEm9DVXcfPXiV12Ve3fOnX3uzDP79zMa95Hlna13KNeMrI3PVqvbmju05naIPWRXFj8j5uvljuMzYv54rTq7viX2mF1Z7KiYa3b94czavyL+hm//PQAY400BJ81suK7cpF2Ve3e+j105d+X5mN1Ej8QcsrzZ2Ihyzcza+Hyxdm281Jo7K9aPvcTacX5GzJ/lqY3PiPl35twh9lS7MiMxM2K+Xt6RmL/s7c8PwDpvDn7etzdAs/Wv3LhdmXe3HTl35DiUfy8jeUdiDlnueD9qdV0p9lO7Mq25VVndeF+OxT/PivWyXLXxWbHG2Zxn1scesiuLzfTmd4n9ZdebvPnZAdjD24M/4ZuboZW6V23grsj5cUXOj7N5z66PZjbXvflDmSvmH6lTWlnTEvuIV6Y1t6JWszcW52bFPDFXbXxWrHEm38z6WDO7WlpxM3muEOt/o4dveNvzAnANbxH+lG9tjlZqXrGZuyLnx+58hx29nl0flb9hL/fofBkX8/dylGbjR8Reen215mbV6mVjcTzOzYq5Ys5sbEXMfyZfa32skV0zWutac3f4dv27nfl7BIDIm4Q/6e6N0mqtKzZ1u/Mdrsj5cTbv2fWZ0Q336FyMG80fzcaPiv3EK6qNz6rVycZG5mbF+qM9zIj5V/OVa2O+2nVGLc/OGiu+Wfsb3va8AFzPG4U/7a6N05kauzd4O3OVrsh5OJP7zNqW8u+lVqM2/lHOxbiR3JnZ+Bmxp+yKsWfUcse5qDU3K/ZQ5szGVsT8K/ni+uzaqZW3NXeHb9e/05ueFYD7eKvwCldvos7m3r3R25Ur5tmRs2Y19+q6EeXfS1YnG/uI4/H+GKvlzczGz4rPWtaKY3F+VitHbfzQm58R+yjzxvsVMe9Kvrh2JcesWp07e8h8u/5d3vKcAHyHNwuvsntDdeTakXPnhm9XnsPO3g4x12r+lTUzymePteL9zNhHLW90zI/ErorPmdWKc1lMT29ta+6jNz8r9nPkjfcrYt7ZXGfWnlGrWRu/y7fr3+ENzwjAd3nD8Eq7Nlhljl35dvS2I0dmV3+HmCfej1pdN6J85lgn3s+MfdTylsq5XuwZ8TlbvfXma0bWteZbc6tiT0fueL8i5p3Jtbpuh6zuN/s5fLv+lZ7w+wLwDt4yvNqOzdax/myew+gmcGS+F7OifN4d+WOOeD9iZc2M8u+krBXrxvtDazzLW4r1anFnxT7ifTTSe2kk/uz8ithXdq2KeUZyxfiRNbtltbOxO327/pX+8rMB8DzeNvB/5z6sjnWr6zMjG8LW3Edv/aqYc6TXnnLtSq7Z+BXlc8Z+y/9GtfGPWs5yPt7HsZ1iP63ePkZiPlbiMr35VbG/eK2KeXq5Ymwv/iqxfrz/hif0sNsT/q4BeB9vHPif1U1YuUneqbcxrI0fWmvPaOU8U7P8HWfzzMSeUfYW+63pzcWrnCvF+SvEPuJ9ptZ/aSTmoxfTm18V+4vXqpinlSvGtWKvFnuI93d7yu+y0197HgB+hzcPBLObsnKTvFtrk5iNRbW1Z/VytvpuKX/LmbUzsWeVzzbynL252hXVxneK9Xs9HVpxrbnSSFxvflWsHa9VMU8tV4ypxd0l9vLtnp7Qwy5P+U0BeC9vH6iY2aAdcaPxM2qbxXifydbtMJOz1n9NGTu65mMm9qzymXp1W/MxR7wv1cZ3yupnY5kyLnuemfU1IzGrYq87asU8Wa44n8XcLfbz7b6e0MMOT/k9AXg3byDoGNmsHfO9uFXZpnGkVrZul9mco73E37IXfxiN26V8nlbt3lxcH+974ztl/bTGozIuXj0jsSMxq2K/O2rFPDFXa+6bYl/f7O0JPezwV54DgN/nTQSDWpu3Y7w2v0vZw2itqzaeZ/L1eorPWYsrjcTsVD5Dq3ZvLnvWLGc2tluvdjZXinG9+MNo/EjMqtjDjloxT5mrNv4Esbdv9veEHs54yu8IAAdvI5iUbeSO+zheGztjdjNZxs6s69mZJ8tVjmXz0UjMbuXfRa1+bfyjtj7e18Z2y3oZmSvVnqllNH40blXs/UytmKPMUxt/iqf095Q+Vv1y7wD8Xd5KsChu7OJ9qTa+qlUrymLj/apdeT6yzXLtzzUjMTuVPcfey5ia3rr4/FncTiP91OY/YkwrtjQaOxq3KvZ9plbMceTJxp7mKT0+oYcVT/n9nsrvAvBd/gWGk+JGr7axqY2viDV7sth4v2JHjkz5fGWNXr3e/G6xz9jvEVNTW5PN1eJ2ijWjmfl41YzGfYzGrYq9nKkVc2TXE8Uev9XnE3pY8Ys938HvAvAc/iWGTXobnNbcrCNPr+ahFpONzTi7vic+X+05Dq253WIvZa9xvCaLL8WctbhdenVavWRz2VjUmy/NxK6KPa/Wijni9VRP6fMJPcx4yu/2JH4PgGfyrzJs1Nvw1MZnlXl6NT9aMbXxUWfWjjjyl89Qq1kbv0LWR9ZjjCnF2MxIzC4jtbKYciyubc3F+ZbRuLNiv6v1Yo6z+e7ylF6f0MOop/xmT+B3AHg+/0LDRiMbwdr4jJijV/NjZH7F6rpRZf7e75uNXaXVQzmXxXz0nuUwGrfLSK3YU2tNa741F43GnRV7Wq0Z16/mudsT+v12/Z74Gz251zv4DQB+i3+tYaNjA9TbDLXmRmTre5uw1tyhN59ZWTMj9l0+Z1Y7G7tCq368omOsFVMajdthpFZ8vtn4bLxnJvas2O9Kzbh+JcfdntLvE3qI4m8zev1Vb3hGgL/Kv9ywUbkZ6m2OWnM9tbWtTVlrrtSbz6ysmRHzl88SnynGXiXWLdV6K+eP/9ZiSqNxO4zW6j1jlMXH+5aZ2LNir7M149qVHN/whH6f0MNH7KN1zcYfa37Jr/cPwD/8Kw6bHZujkc1Sa66lta5VtzYejcYdZmJXZPlrv3MWe4Xeb1T2VcbFP8f5TC3XFUbqxH5asaW4Zmb9TOxZsbeZunHN7PpvekK/36ofn713jYhretfTPLk3ANb5Vx02KzdLvQ1Ua66lt6ZWNxtracXGXK3YHbL8x1j5vFncFUZqxb5ifG08MxN7xkid+Eyt2CiuG107G39W7HGkboyP19M9od8768fnbV07xdy9607fqgvAffwLD5vFjVNvQ1UbbxlZk9XNxnp6sSs5V9TyH+NlH7XYnUbrtPqqjWdmYs/o1YnP04vPrKybjT8r9tirG2Pj9XRP6Pfq+vEZe9fdYv3etcsVOQF4Lv/aw2bZJqq3waqN14zGZ3Xj/YiRNVmtnWp54/jVfXzM5C/7ieuysZbZ+BWtGtlzxPsRWZ6e2fizYo+t2jEmu57uCf1eUT8+V+t6qthn7xoxGw/A3+FffrhAtqnqbbZac9FsbFm710dLb12s0YufVcsXx6+qfxjNXfaR9ZSNtczGr6jVqD1DnBsRc42sm4ndIfZXq53Nx7Fs3dN8u99d9WOe1vXr4vO0rhgPwHt5C8AFahus3uarNVcajTvEjV+vj5bWumwu1j6jlaOcK2u21qwazVvGZT3F+54sx25Z/l7d3nwU40fWjcbtEnvLatfm4nhc9zSx12/0u1o79t273iA+85ueHYA+bwS4QG2zNbIZa80dRmKiuBlcyXGora2Nf1xZ93DMl//dUTcazRfjsn7ifc9s/KyYP+s5MxLzEfPFq2YkZqfYV6yfjbXWPtkTep2pH/ttXfyX3wOAg7cBr3XlhqiVt7c5bc0devM1OzfHtRzZWHSmh96aY76MO1MvM5KrFlP2Eq8Rs/GzYk+j9UZjs5je2t78FWLN1hXF+SzmSb7da6927K910eY3AsCbgNe7auPYytnbsNbGD735lt0b5pgj3vfM9jISl+WbrdMykqcVU/Yy29fKmhkx/0ytkdhaTKtWbfxKsZ/alYkxtbin+HavWe3YU+tijt8M4N28BeB/dm8me7l6G9jZ8Rm7N9AxR7wfMdNPL6aWZ6ZGSy9Hb/6j7GUkvrSyZkbsa7TOyJrWfG19Nna12Et21cS4Vuy3xT7v7jXWHrk4z28J8F7+9Ydg18ZoJEevVjaXja3YvaEu85zN2eutNl6qrS9zZ/Mjemt784fVXlbWjIo9zdZora2NH2prs7GrxV7i1RJje/Hf9M0+Y+3WxTX8tgDv419+qNix8RxZ36sT5+L9qis22LvzfWQ5R/LHNVGWd0RvTW++VPYws+5jZc2I1X5KtfW18VJWP97fIfYRr5oY14odtSNHze5eR8W68eI+fnOAd/EvPnSc2RyNrBvZ9JZzrbhZV226d+f7iH2O5O/1EXOO6MX35qOyh9V1O632U6rlyMYycf3Iutbcilg3uzIxphY3Y0eOmt29jog176xNnb8DgHfwrz0MWtmkjsb3NsHlXC1mVa/2iitylkbzz8T04g6t2NZcTVl/Zv1s/KiVXjIxR7zviX301rbmZsWatSsTY2pxM3bkyOzuc0SseWdt+vxdAPx9/qWHSTMb1tG4j95m+Bivza+6aiO+O1802vNIzMeOfK25lrL2zPqVNT2rvUQxz0rOuK61tjU3K6sZx2r1YkwtbsaOHJndffbEenfVZY6/F4C/zb/wsGh0kzQSc+jl7M2vumpDvjtfNNJzb750Jt/I2ppy7UyO2fielR5aYr6VvKNrW3OzsppxrNZPnM9iPmrj0WjcipE+d4m17qjJOf5+AP4m/7rDSb2NbGsu08rXmjvrik35FTkzvTqtuWg1V218VFl3NM/Kmpbd+T7O5hxd35qbEeuVeeN4VjPOZzEftfFoNG5W7PGqOh+xztX12MffFcDf41912KS2UcrGemq5PlpzZ1y1Ob8iZ6ZVpzZe0/otWmNxfEasOZprNr5lpX7PjpwjOWrjs1q14lycn4kZNRM7o9fjLrHO1fXYz98ZwN/iX3TYLG6WVjZOrY1ybXyHqzbpu/PV1Hqvjfdk6+J9bWxFWW8032x8y0r9nh05R3LUxme1asW50ZgoG6uZiZ3R63GHWOPKWlzP3x3A3+Bfc7hIudld2TjVNszZ2Ixa3kNvftUVOTO1/rOxEWW+LEdtfEWsM5JzNr5lZ65DL2c2FvVyfNTGZ8Q6Wc44H2PiXJw/YkbNxM7o9XhWzH9FDe7n7xLg9/lXHC5W2wDH+0y2Nt6fETfo2bXLFTlrslrZ2KjWb5KNndGqVTMbn1mpO2Ikb2380MuRja3o1fmIMWVcHI/zR8yM2fgRsb/dNWLu3fn5Pn+nAL/Lv+Bwg9pGOBuLsphsbKe4ed9Va3e+lqxWvJ+R/R7xfodYZyT3TGzNbM1RI3lr46VWnni/qlXjEGPK2DiW5cjGamZiZ/R6PCPm3p2f5/B3C/Cb/OsNN2ltiGvjhzgf768QN/G1a9bqulWx3zP1Y44zuVpW8s/GRys1R4zmbc19tPLE+xWt/FGMPeLjWJYnG6uZiZ3R63FVzLszN8/k7xng9/hXG27U2xiPzrXidur1+1HGjMR/jMTsFHu78toh5hzJOxObma03aiZva76VJ96vaOWPYuwRH8dinnjfMxs/qtXjiphvV15+h79vgN/hX2y42cgGOZuP67KY3c5s6OPacn02NivmfuJ1RszVyzcTmzm7vmYmb2u+lSfez4q5e/libOuK62bMxo9o9bci5tuVl9/j7x7gN/iXmj/nFzYgoxvlOB832XH+CjvrxVxlzjh2xzWrXBdzjVyzZtfPxJZm68yayd+ar+VprRlRy9sS19SuuGbGbPyIVn+zYq4dOfl9/h8AeDb/SvMn/cIGZHTDHGO+sdm+ql58lplr1ZkcIz3EmNo1Iq7prRuNi2ZqrJjNX4up5anFj6rlbYlralcZP2tlTU+tv1kxz9l8/C3+XwB4Lv9C8zVXbxqvyrvTzG9Qxs2s26Gst6NmzLcj54yVumX86Nr4jLWr5arY0uq6UbP5azG1PLX4ETHnaK64pnaV8bNW1vTU+psRc5zJxd/l/wuAZ/IvM48QN5I7Ng5n199l9nnjbzS67qwzNePacn02dodaPzWz8VFcX7uiOJ/FlEbjSjP5V6zkz+JiniMmix2V5RsV12ZXGTtjNr4n9rWaP+Y4k4t38P8HwLP4V5lHi5vM2c3mTOw3rT7b7JqzRmvGv6/R+Lut9DgS2xNzta4svmU07hBzj66bsZo/i81yZXGjsnyj4trsOuJmrazJxD5ibzPi+tU8AMD3eHPzk+IGtLURrY0/Te85ovjso+vOqNWL4yu9rK47I/bcqj8Ssyr2MHK1jMZ9xLwja2at5s9is1xZ3IiYazZPXBuvMm7Wypoo5qj1NyKuXckBAHyftzd/RtyYlhvUp25UY6+7rivFWrtq7sw1Iz5HrX5vfpfYS+1qGY37mMm76kyNGJ/lijGjslyzYo4s30rulTWluD72Fudb4rrZ9QDAc3iD8+fFTesVm9eY+45rpPYuMe8VNT6uyttS1mvVr41fKf7WtStqzUW9XDucrVGuiblWc35ckSPmO5N3Re1Zst5GxHWz6wGAZ/EW5zXipjVuaMuNbRy76qoZiTnEnNk1K66POVpzZ12Rs6esWXuubOxO8TevXVl8S239TmdrxDUxX5wfEdev5PiIOWK+M3lntdZkvfXENTNrAYBn8ibnVUY2r3GzO3JdYTR/jIm9jeSJca3Yw2z8jCtytmT14vNlMXeLvYxeLTG2F79iR/5yXcy3kvPs+lLMVeZczT27rhef9dYS40fXAQDP5m3O67Q2sU/b5I5uvGsxcfPeulbsyJG5ImdLrd5Vz3dG1lMcy65MjCnz7ZTVWFH2F69ZZ9eXYq6zeWfWjdSJPa3E99YAAL/BG51XipvZJ29wRzbgo/Px2mF3vsNVeWtqta74zc6I/cSe4lwtLouNc7u06sw41sZ8sznPrM3EfGdzj66biRvtKcaOrAEAfoe3Oq90bGh/ZXPb24i35kpxUz+6rmVnruiKnDW1Z7jy+VaN9hTjYnxtvJzfoVdnxrH+TM4zazMx39ncvXWzuUd7inG9eADg93iz80q/uLFtbchbc5m4wZ9dH+3IUXNFzppYKz7XXX30xJ5afcW4Mj4bi2rjM0bqzIj5ZnOeWZuJ+c7mba1tzdWM9BVjWrEAwO/ydueRrtp8xrxX1LhSa2NeG2+Jm/1W/p4za1uuypuJteJvclcfI2Z6irG1q6Y1N2K0zqiYbybn6rqWmPNs/tq62njLSD8xphYHAPw+b3kebdemtLW+Nv5Utd8jG8tk6+PvnF09s/Ezrsqbic9x1Iz33xZ77PUVY7OrpjU3YrTOjJhzNO/KmhEx75n8cd3ZXK1+4nwWAwD8Hd70/JTZjepM3C/JfoN4X8riM/H3bV2ZkZhVV+TM1J4hG/u22Guvtxg7uu5jJKZmttao2bwxfmTNqJh3NX9cE+9ntfqJc3EeAPh7vO35abWNazbWMhP7FNmzx818nB8V149c2drdrsob1Z6hNv5Ntb+Hmhg/uu5jNC5aqTViNu9s/IyYe7VGuWZlfVTrJ47vqAUAPJ83Ptt9ayN5djO7subb4jOfef5MzLly7XRV3qhWpzb+TfH37vUWY0fXHUbjSit1RszmnY2fEXOv1DizNpPli2O7agEAv8Fbn+2+sZnMNrErG9zRuKeIzzjzrDNi/qxWHI/XLlfkjGo1rnqms1b6imtm185YqTEi5m3ljnGt2BUx90qNlTUtsZfaBQC8hzc/l7hrUzmzgR3d8Pbmvy17jrihv+oZYo1WvTifXavOru9p9dia+5b4u/Z6i7HxGjEa97GSf0TM28o9Grcq5l+ps7KmJfaSXQDAu3j7c4mrN5ZnN6+tTXC8f4Jar6XWM+0Wa2V14/jINWNlzahWT625b5r5LWNsdvWMxBxmc88YzT0atyrmn60zG98T+8guAOB97AC4zBUbzKs2rnFjfFWdGSt93N1/rBdrZ2Mja7P4aDRuRSv3TI93in21esvi4lhr/WEk5mM274yR3DGmFndGzD9bZza+J/YRLwDgnewCuMzOTebdm9ZvbZR31N2RY1b8uKhdPTE+XlFt/KxWzY/e/Lf0fq9DLS6Ox/lMb/5jJt+smDvL35vfJdYZrTcaNyP2MNMPAPB32QlwmR0bzW9uWO/YNF9R44qco2Lt7JoR18arjNkp1oh6898Sf59af62YOJfFRCPzo7lmxdxZ/t78LrHOaL3RuFGx/kwvAMDfZjfApf7ChnP35vmODfnV+XviM8ZrVcyTXTuM5BuJ+YaR36MXE+dbsYfW3Mdonlkxb8wd5+L8TrHOSL2RmFmx/hU1AIDfZEfApf7KpvPsRvrM2lXfqBnF3213TzHnrtwjuUZiviH+FrG/1lwpxsUrUxv/GFm/IuaN+WvjV4i1RmqOxMyItXfnBwB+m10Bl/tLm8+ZDfVM7BWe9AEQe9ndV8x5Nu9InpGYb2n9Fq25KMaWa2rrs7GPLMcOMW/MXxu/QqzVq9mbXxFr784PAPw2OwMu99c2oL2NdWvubr1e7xY/THb3FvOu5h5dPxp3t/gblP3VxmtifFyX3Wdq68+Kecv82diVYr1e3d78rFh3d34A4PfZGXC5v7gB/ZUN9hP7jD3t7i3mXck9unY07htqv0FtvCWuKdeW/41jpWztDjFv7COOXSnWa9Xtza+IdXfmBgD+BrsDbvFXN6K/sNF+4gdB7Gl3bzHvbO7RdWdqXC32dvSXjY2I62o5anO18R1i7tp1tVivVbc1tyLW3J3/133jt/hGTQDo8XbiFn95I/QLG+4n9hd/tyv6W809s2Ym9m7x+eM1K65v5YnzI2tWxdzZdZdYN6tfGz8j1tuZ+6+4+ze5ux4AjPB24jZ/fTP05I33Uz8MYl9X9Bdzj+S/KvZu8bnjtSLmaOWKMb34VTH3/7djL8iyo0qiROc/6n623+3sq/Li/xfyZRZWtSUIAjJToBOKVThuaPzQtR4ca3T+W6xck5VjSZJUwx1Ky3zhQHTyAfzU2ljXjPqYO5e/tN1PbfuVOO9RtTJXLB/bpNq2Yu5QrMJxOX7oWi+ONTL3bVatzapxJEmq5Q6lZb5yIDr5IP6GumbVyNyp/CVtnmrbr8Z5j6qV+VJ5S9q0Ym7GShybNfDvXhxndP7brFqbVeNIklTLHUpLfelQdOJh/PSXBNY3o07mDuVP3Qupbb8a5zuyVuaM5c7d7/HMyXFGj5XDsVkD/+7FcUbmvtXsNZqdX5KkHu5SWuprB6MTD+an1UNcsxm1Mjfzx66ntPRZifMdWSfzhvLzHu/3eObjGCPHKcGxQ7WNwjFG57/V7DWanV+SpB7uUlrui4ej0w7np9VDfKGZUStzP/OHruW09FmJcx1ZJ/OGxuD1UJtWzzzMPSJ/DY4dqm0UjjEy9+1mrtXM3JIk9XKX0nJfPRyddFA/qZYY1jir1lB+/l0ilOckrI818u8aoXXjOLlrPZibsRLHZozCvKPz327WWs3KK0nSKO5UWu7rB6RTDuun1JHCl5tZ9TJ/61it/VbgvEI1hq6VePbjGLEIte/B/KPy1uLYjFGYd2Tur5ixZjNy9jqxJknSPu4KHzTqsNhz8Gzpc5MTDu4n1FCCdc6ql/lbxmnttwLnFasxdj2FfThOKFLtWzBHb75WHHtGHcw7Ov9XzFizGTl7nViTJGkfd4UPG3lo5EE0lzd3/wu4XiXrNtrOsWuwzln1Mn/tGD19Z2NtqfpS90JC7TkWIyR3P4X5e3L14Ngz6mDekbm/ZvTajc7X67R6JEn7uTNo2gGSB1SOwb9vxTWoiRVWj9eKazOzbuavGaOlzwqcT66+3P2nWD6OVzJ2SZsQ5m/N04tjj66DOUfm/qKRazcy1ygn1iRJ2sudQf9nxUGSh9bZ463COc2IWVaNMwrrnVE3c9eMUdt+Fc6lpL6SNj+xthyzZPySNsTcLTlG4Nij62DOUXm/bNQajsozymn1SJLO4O6gf1l1sPzl52F29ritWGNp1GDfUMywYoxRWOuMupm3doza9itwHqW1jWjHcUvGr2n7h+1r+o7EsUfWwXyj8n7dqDUclWeU0+qRJJ3B3UFRKw6Ysdw84MbajcYxS2MGjhGKkWblHe1XH9diZO3MycipabsK51BTW0nbXBuOXVpDaVvmLe03GsceWQfzjcip/+hdy97+o51WjyTpHO4QKjLrsFmTkwffmr5PzFEaO7GWUPQanS9kVN5fHtY8qvZQLo6RGqe03UqsqbauXPvc/T8cv6TPn5L2zFvSZwaOPaoO5hqRU//Vu5a9/Uc7rR5J0jncIVRlxqGzJx8Pw79cvFYab8CaQ9FqRI6UUXmfeTj3EfXH8nAM3n8qabMS626pK9Unde+H49fUkWvPnLn2s3DsUXUwV28+/VvPmvb0He2kWiRJ53GXUJORB9BReX54SGbchHMLRa2evjmjcjIP59xbfyoHxwi1+ZO736MlJ2tuyfEn1i92nVhDTS25Prwfa5fT0ueHYzNaMEdPLsW1rmlrv1lOq0eSdBZ3CXUZcRjt6RvSW89b8eUgFCVa+pQalS+Uh3W31l/aP9cud79XbU7WU9v/KdQ3dC2ENbTUEuvHnKE2pXr6paIFc7Tmme3Uumq0zKGlzywn1SJJOpM7hYbpOZi29nvqGf82fFkIRUppu1qj8qXycJ418/i1K+3HMZ7tY9dHqsnLemr6hrA//05hHS31hPoxH+/X6OmXilrs35pnhVPrqtEyh5Y+s5xUiyTpTO4UGq7lgFrb/qllvC/hi0MoKHe/1ahcuTysv3Qevza1fRihezPU5GWNNX1jmIN/p7CWmr4/7Mt8rXl/WvpybEYt9k/lSN1bYff4o9TMo6btbCfVIkk6l7uFpskdVqmm7Z/a/Aq/TDBibXuNyPFTkov15+YRm3sJjvHrF7o2Wmle1lLaL+eZpyYna2mtif1D0aOmP8cNRQ32zeVI3Ztt59ij1cylpu1sJ9UiSTqXu4WmKzm4/snd/ynJpTy+VOSi14gcP6W5OIfYXHgt1z6G/RizlORmLSV9Sv1y1eZkPT11MUdvvp+a/hw3FDXYt6R/SZtWqdype29UOp/SdrOdUock6XzuGFomd4iNXf9J9VU7vmCkokdv/6eaXJwD5xLLFWpbguO05qmVy89acu1rteRkPS05npinN99PaQ6OG4pS7Ffav6RNi1ze3P23KZlPSZtVTqpFknQ2dwxtETvMxq6Frms8vmyEolVP35CafJzDcy6xPGxXg+P05KqRys86Um1btOZkTa15/jBHTy4qycNxQ1GK/Wr7jpbLmbv/Rrk55e6vckodkqR3cNfQVjzY8v892OzDl49ntGjtF1Obj3PIzaWkTQ7H6slVKjYG64i169Gal3W15Phhnp5clMoVGpPXSuth+9J+PzVtS+Ty5e7XGp2vVa6O3P1VTqlDkvQO7ho6wvOA23Lg1Vx8EWn5bFr6pLTk4xxS80ndq8FxevPlxPKzhli7Hq15WVdrnj/M0ZonJJUrNCavldbD9iV9qKVPTC5X7n6p1rnOlKondW+VE2qQJL2LO4eO0nPg1Vx8Ian9jGrb5/Tk4zxC84ldb8FxRuRMCeXn+KE2vXrysrbWXOzfkiMlli80Jq+V1MO2JX1CWvqElOQpaZPTOs/ZYjXFrq92Sh2SpPdw59ARnoe/3oOv5uFnU/P51LQt0ZOPcwjNJ3StB8cZlTeG+Tk274/Smpu17c6TEsoXGo/XSmph21z7lJ6+f0r7l7aL6e0/W6i+0LXVTqhBkvQ+7h7aKnXAHXEA1lh8Man5fErblWrN9+zHeTznw797cYxReVNyc52hJzfra8nFvi05ckL5QuPxWq4Wtsu1z+np+6ekf0mbmN75rRKqMXRttRNqkCS9j7uHtig9+I04BGus52dS8/mUtKnRki/Uh/MIxSjMO2MM+uXmeLPG7MnN+lpysW9rnpxnPo7x/G8oQtgm1bZGa47SfqXtaNT8VnnWekLdq2t42+clSYrzaa6lWg4Row/E6sfPJPfZpO61askZ6sM5hGIk5v7lD10bIZZ/5BhPvflZY20u9mOM9MvH/KHrbENsk2pbozVHab/Sdk8tfXZ71nxC/atqGPU9lCSdw6e6lhhxiBh5KFa/5+eR+2xi13vU5oy1/13nPHJz6sH8oTFS92pxrFF5Y3rzs86aXOzHGOmXj/lD19nmifdj7Vq05KppX9u2pv1pfrXvnsPs8Ud/ByVJZ/HprqlGHyI8mJzl+XmkPpvQtRFK86baPe9xHqk59WDuXP6atjHM0ZqnRG9+1lmTj31CMVIo9/O/sXjivVCbHjW5asYubfenJu+pTpnDrBpmfPckSefxKa9pZh0inoeUWWOoDD+L2OfCv0cpzZtrx/ucC++PwPw1Y/T2qe1ba0R+1lqak+1/fULXRgjl5P+HovT+CDX5ZrQtbXe6GZ9NrRnjnzAvSdI6PvH1WrMOy6rDF5fQZ8K/RynJ29KGcwnNaQTmbxmjtC/HybXv1TsGay3Nx/bPPqFrvUI5+f+hKL0/SknOkjZPufaz5rLLCfMZNf7M75ok6Ww++fVqHmLO8PwcQp/JrM8nlzd3/yfUjnMJtRmBY/SMk8rDe7w/2ogxWG9JTrZl+9j1VqF8/P9Q5O6NVpK3pM1Tqv3Mueyye04jxt49B0nSfu4Cer0Vh2fl8XN4fh6zPpdU3tQ9CrXlPGZ9v5ifY/DvGszLmGnUGKw5l5Nt2T51r0Uo3zMv77NdKGZJ5U7dC0m1T917s9mfT07r2Cu+W5Kk93A30DU85Oz1W/fn5zD7M0nlTd2jWFvOYdZ8mPuZf9RYzM9xZhgxBuvN5WS7UNvc/VKhHLG/S2OmVP7UvZBQ+xVz2Gnn/FrGXfW9kiS9i7vCR916KPDA8x+75v8b9/k5zPw8Ynlj12Ni7TmH51xGz4tjPMcZgbkZM4zKzVpTedmmpF2rUI7Y36UxW2iM0LUc9llV/04751gz7s46JUnnc4f4uBsPCqsP1CfaOe/f2PwcZtQUyhm6ViLUj/WH5hG73oLjjMr7hzl/eUPXRhmVkzWm8rJNabsWof6xv0tiBY7Dv0txjl+w8nN6Khlz9fdIkvRe7hT6/248OHz9QLRr3nwxYPRifgpdKxHrx/pT88jdz+EYrXlCmJe5U/d6jMrH+mJ5eT/U5qe0XUyoL69xjFisxHprcW5fsWu+qTF31SRJei93Df3DrgPpLLfNp8bOOfMFgdHrmSP2/7VifVl76RxK2xHHackRwpyxvCVtaozK84e1hfLyfqjNU2k7So3Ba2wbipV+47WOu6vu3XbMOTTeV9dfkjSGu4eibjlgPA9LN8yn1O65/sbn+o/6HJ75n/9tlerP2lNtqbdPbd8Y5svlrGmb0tv/iTWFcvMe71NN26dUH17nGIzVesZu7XeDHXOPfY94T5KkUu4eytpx6JmBh6cv2D3X55qHotfoXDGsu3XMmr4cq6RPCnOV5mvp89TTN4T1MC/v8X5Ibfs/qfa8zvyM1VrH3VnzCVbP/TdWbNzQNUmSctw9VOyGw98Nc6ixe57PtX6u/ajPYVSeP7kcrDvXPieXg2Ol2j7F2jFXrF3MiL4jsA7m5vXScUe253XWk+q7QuvYrf1usXL+Jd+R1D1JkmLcPdQkdzA52QkH8FV2z49rzLXn/Vojcjyl8rDmUeOmcnGsUJun1H3mSbVNYY6SPKXtSnF85uf1krFr2pe0fd5j+1zf2VrG3l3zCVbNv3SckjaSJJG7h7q8+VD4ptp7auzpOwLX+LnuvZ/Bs29Pnp9cf9aca18rlJvXUmPm7jF6MFcqX0mbGhyXuXm9dNzSPjVtnv8fih1axm7pc5sVa1Dz3ShpI0kSuXtomNJDy0lqDlu7tdbY2m+U0Po+1z10v1SoL/+ukevLmkPjj/LMzfFCY4auPbF/rn0p5ozlTd1rwTGf+XmtZtySPjVtnv8fih1qx65pX9ruFDX11qxDi9rvRWk7SZKe3D00XM0B5gTPQ9fpdbfU19JnpNjact15PyfVJ3Y9p6Qfay7p0+KXl2OFxuTfIexf0qcGczN/6FovjvfLz2s145b0y93/wzyx2KF27Jr2pe1OUVNvzTrUavlO1LSVJOnH3UPTtBxodnpLvS31tfQZKbauzzWPtYnJtU/diynpw3pzdbRiTo73u892Mexb2q8Wx3jWOXpMjpOKGrm+qXs/zBGLHWrGrmn7p6btCWrqrV2LUq3fh9r2kiT9cffQEi2Hmx1aD2Kr1dZX23601Jo+1zzVjkra5u6HlPRhvSV9aoVycsyasdmntF8rjjVrXOaORa1Y39j1ENbA2KVm/Jq2f2ranqCm3tq1KNHzfWjpM9Np9UiSwnxaa6nnYacmVto5do2a2mrazpJaT655rN1Pabs/JW2eStqz1tJaasTyccxYO2Kf0n69OObosZk3FrVi/UPXYpiDsUvp+KXtnmrbn6B0nqXtavTkbO03y2n1SJLCfFpri+ch+G1xkpp6atrOkFs/rnNJ21Iz2rLW0n4lUrk4ZunYbF/SZySOPbIO5gtFi1AO/p3C/jV9ZyqpobXW2vYnKJ1nabtSvfl6+s5wWj2SpDCf1lqm9UD559n3tNittIbSdrOUrBnXNtY2dS+mtH1Nu1CMkMvDMUvGZttc+xli4/N6S23sz2jFHPw7hTXU9J2ppIaSNjGt/XYprbdnTWhErt7+o51WjyQpzKe1pjrlwNvqWX9p7FAybkmb2XJrxLWMtY9dzynpU9Lmh3XW9E3J5eGYJeOzXartTKU1sF2q7R+2ZfRgrpJ8bM/YKVdDb52t/XYprbdnTZ561/dPT9+ZTq1LkvRfPqk1Re/h5lTPg1tNrJAbJ3d/hZL14NqxD/+uleubu//EGntr+0nlCK1FKIj3Q21Waa2B9TMHrzNaMU9JLrav6Ttbro7c/ZyevjuU1tu7Ln9GfQ96+89yal2SpP/ySa1hRh1s3uY579KYJZc7d3+FkjXgej37lPTPyfXP3X9ijTV9Y2I5eJ3jMnJtdxldB/OF4teuVShfCtvX9J0tVceIOnv6rlYz15q2ISPW9mdEjhlOrUuS9F8+qdVl5IHmFs81qYlRUrlS91YpnS/Xh9ErlSN1j1jXiPpC/UPX/nBcRqrdTrNqYV6O0TpeKFcM2zJ2S9WRuleqt/+fETlK1My3pi2N/vxH5Rnt1LokSf/lk1rVRh9kbvdcr5poleqburdKzRy5JjV9S8Ryha6lsLba/k+xvrHrfzh2aew2ox7mfObmtdoxS/uyXUmflWK1xK7XGpHjz6g8KTVzrmn7NOPzH5lrpFPrkiT9l09qFZlxgPmy53qWRo1U+9S9VWrmxHWo6VuK+fh3DmvrqTHUL3SNOPavD6/x/m6j6+EcY/lT92JK+7BdSZ+VYvWErrUYkeNnZC565i4Zp3V9WvuljM43yql1SZL+yye1kmYcXPRvv3WujZTY/dj1lUrqf+K8a/qWeuZsyc/6WnL8YT/+HcOxOZ9QnGBGTcyZyl3S5qe0LduV9FnpWcvzv6PqG5XnZ3S+n2fekjFa1qilT4kZOUc5uTZJ0v/4DwD6t9+BxU18r+fnUBpUem2HZ82cR02M9KynFutqrfHZvqUvo+TebqPrYr6SvCVtW9owTsBaRtc3Ks/T7Jy5/C1rVNu+xqy8I5xcmyTpf/wHAP1Hy+FGaz0/IyMcI/zytORjPc9cpfme7Ur7PHF81sDrpxhZF+dZkzvXvvZ+qu0urGd0jaPy0Mi8zMW/n373atZo9JrSrLwjzKptVl5J+hqfph8384CiuZ4HTOOf0as1D+tgHv4d8rufa5fC8VNxitF1MV9t3li/2PXY/VTbXZ71sL4Rdc6c76i8zMO/f57XS+fFNZ1hZu5eM2qbkVOSvsonqnSR58HTaH+89fRnDcwTuvbzux67X4rj5+IUI+tirtac7M9obbsLa+Hfv2u9RuSICdVci/35909urWjV5z07f48Ztc3IKUlf5RNVusjz8PmmiPndY1v2z0WL1r4cO5YndD10rRXHz8UpRtXE+fXmZJ5QTl4PxW7POlJ1ha7V6O1fonWMUL/ctdRa/ZS0GWXFGK1G1zY6nyR9nU9V6QLPg2fuEPq7Hru/WqrWP6n5cL65qNHS5w/HzOVhu1TbWszLCLU5wYh6OK8ROf8w1zMfr4dit2cduZpy91Na+9VqGSfUh9dCf/Pa0+rPeNU4rZ7fsR69/X9G5ZGkG/hElF7seeisOYCWtlshV0vJvDj/XJSqbf/D8UrylLRpwRpi9cSu75Cqswbz9Ob7Yb6a2K22ntJ21NKnVe1Ysfa/66H7uXXI3R9t5VgtRq3HqBwj8kjSLXwiSi/0O9AwarT0mSFXf+4+cU1SkVPajjhOSZ6atjWYNzVG6t5quVpLMEdPrifmy8Wzz26h2krUtP1T275X6Xipdqk1ab03y+rxUkK1hK7VGpHjz6g8knQLn4rSi/wOmowWvf1HStWRupfCNUpFSkmbEI6RyhG6z76hNqWYI5Urd3+l3lo4355cT8yXi2ef3VhXjZo+NW1HKRkz1SZ3L3Q/dn22HWNSau6x66V6+/+kapSkr/KpKL3A7xATih4jcoyQqiN1rwTXKxcUu57DvKk8sXvsOyNCStqsMKIO5ujJ9cR8qWCfnUJ11SjtV9putNy4qfu5e7zfu5Y9doz5k5tz7n5OT18amUuSbuGTUTrY84DJGGF0vh6xOmLXa3H9chHqW4s5Yzl4j38/Md/qWK13fPZvzUPMVxM7jaijpH/u/kyxsWPX/+TmxPsj1rHHjnFL5vu7n2uX0tP3qaReSfoin4zSgZ6HS8Zos/LWCtUxY95cz1w8+9RirlCeEeOUYA2jYoWe8Vhvax5ivtrYYeT4uTypeyuExg9d+/O7Hrv/5znfkevYavXYJfN93s+1jWntFzIylyTdxKejdJDnwZIxy4oxSoTqCF0bhetbGrXYnzli10djDaXjsm0uZugZg31b8xBzxSLWfocZ48dyxa6vxBr4N6+F7v/w80u1XWHV+DVzZTv+nVPbPqWmbkn6Gp+O0gF4sFx9yFw5VgrrWLEOXO9c1GL/Zx7+PRtraBmbfVMxUk9u9m3JEcJ8oUi1X23W2LF8sesr/WoI1cJr/Ptp92dHs2uonWeobehaSm37lJG5JOk2PiGljXio3HXA3DUusYaVdXH9c1GDfRmrcNwRNTBPKnq15mO/2v4xzMcIKWkzw+wxQ3lD13YIzZt//6Suh/LsMrOO2tyx9rHrITVtc076nCTpRD4hpU2eB8oTDpcjx+/JE1qPnnwtWEMqSrAPYyWOPbIG5sxFi5b+HLe2fwzzMWJK2oy2YkzmnzlWLdbCv39S1zm/nWbU0TK/VPvUvafSdqVG55Ok2/iU/JjTDjFf9PwMZn4eLTlH1tKaK7Qurbl6sZZUxLAdYzWOP7MW5s9FiRF9avvHMBcjprTdKCvHe44xe6xSrCdVV+jeqrWrMbKW1rnl+uTu/5S2K9E6F0n6Ep+SH/Y81Lhhzsf1nr3uLbln1FSbL7Y+tXlGYk25ePbJ5diBNayqheOlIqWm7Q/71PSNYa6avDVte60c62f1eCnPOnI1he7vWL+UUXX0zinXN3f/T0mbGqPzSdKNfFLq/zwPOW6i43BdV61v6xgz6qvNGVqnmv6z8DPMBfF+qM0KrGFHPRw3F5S6F8J8NX1jmKs2b237VqvGeVo9Xsqvjud/Y7WFru9Yv5QRdfTOp7Rvql3qXoveOUnSV/ikVNTz0OPGWo9r91zDFWvZOsbMz7o0L9frd+0U/Exzkeu3GsffWcsP66iNHLYv7RfDPIwSLX1qrRgjZseY9Bs/VEfNtRPm8tNTx4h51PRPtU3da3F6Pkk6hU83VXkehNwcw7hGsbWKXR+lJ/fM2kpyh9Yt12c1fr4lEeu3A2vYWUsI6yqJHLYv7RfCHK35WvuVmp0/Zde4T7kaeC/0dy7Hai21jJpDbY5Y+9j1VqPm92dkLkk6kU84dXkejr6+YXItStcld79VT96Sunul8ofWLtV+h2d9/LxbYjWOv7OWEqwxFTFsl2ufwhw9+Xr65szMnbNz7J+S8Z/32faEOVBtLbXtY1ryhPqErvUakfO0z1mSZvFJp6Geh6WvbKacb8vca9qW6s1ZO4cWsTFia8i/d2ON/PxrYgfWsLOWGqw3FsT7sXYlmKMnX2//mFl5a7xl7Gc7/n9NnhVKaxldd0su9uHfI/TOs7e/JL2NTzxN9zxA3bTJcl69c+zpG9Kbq3c+NThObGz+vVuoxp/nHEpjNY6/s5ZWrJtR2rYG+4aiVk/fmBk5a+0av2XcX/vnf09YQ8rVMqPe1nzsx79H6MnZ01eS3sonn5YLHap4bcYBZhTW2FpvrH3seq0ReVrm1eM5VmhdV9ZSijUSvyMlsRLH3lHDCKyfkWtXg31DUau3f8jofK1W19Az72e/njwzxeqZVWtvzud6jtY659Z+knQDn37a7nnImh09mGtE3ljf2PVSvXX9jJhjLa7tc+yVdZRijTGcUy5W4bg7ahiJcyiNGuwbihYjcvyMyjPC6jp6xnv2PWkNn0L1zKpzRM5Ztf2pzTuzFkl6C5+CWup5oCrZiNn2tBghlqdnjJH9euroEVrnHXWUYJ0hz/mUxgocc/X4s3AuuSjFfrFoNSLHn1F5RlhZx4h587PsyTXDs57Z9fXmjq0h1zcUOaXt/tS0laTb+TTUVLUb+myspzVGyuXL3Q9p6fPDOc6ad05o3NU1lGKdIc82z7nlYgWOuXLsmTifXJRgn1S0GJHjz4gcI62qZcQ4/Ax68422oq5cfq5PS/QqzVHaTpK+wqeihuHmfsumu2I+udy5+1TbPuQ559nzD4l9l1bXUYp1Eu9zfqmYjeOtHHsFzikWJdgnFa168/T0nWVFPaPG6F3/mWbXxLmnokRN2xoleUvaSNIX+WRUEx4Ebt1kV84vN0ZNHaXtSuz6nDnujhpqpGoruVcSM3GsFWOuxrkxctg+Fz168vT0nWVFTSPzr6i31syanrlH5h+d7yeVc9aYf2bllaSVfJKpyKzDwcl2zLdkrFFtauxYiz8cl3+fJlZb7PrPc165mIXjrBhzB86NkcK27Be61qonV2u/2WbWNDr3iWs4o56e71mJGXljOWPXR5qdX5JW8Emmf+GB4Isb3q65l46Za5O736q0vlFCn0Po2ilCdZXW+2yXi1k4zuzxduIcGSFsE2ofu96iJVdt+5Vm1TV6zqPzjTCjpmfOkXmfZuQO5QtdG23FGJK0gk8z/X+zDwFvs3MtSsdN1Ri73mv19yQ2XujaKVgb/055zjcXM3CM2ePtxPnForRPrE2v2ly17VebUdvonKM/wxFG1rJyfqPHYD7+PdOqcSRpNp9mEqw8UMTUjB86yNX0r/Ucb+Y4f1LjxK7vxrr4dw7XNxUzcIyZY+3E+aWipH0sb6+afDVtdxld24z5nraOo+pYPa8Z4/zyzcidsnIsSZrNJ5r0sPJwlBOqgQe42hiBufj3SKnaU/d2G7HuzJGKkZh71ji7cW49kco7QmnOkja7ja5vdL4/XO/R+Wv11tAyl9J2KTXjlaidw0g7xpSkWXyiSf9rx+GCB7OSSGHbmqgR6sO/R0nVmLq3U8/aPjFPKkZh3hljnILzaw3K3W9Rkq+kzQlG1Thjvsw5On+t3vGf86nJU9M2pnbMlJG5au0aV5Jm8akm/c+/D32j8RBWOl7ufkysH8euiVAeil3vEavhJ3d/l1F1PfPkYhTmHZ3/FJzfc568lgrK3W+Ry5m7f5JRNY7K88Q1nDFGjdbxe74Pte1jWsb+w36t8xhl17iSNItPNel//n3gOElLXTV9noer1qDY9RapcX5K2qw2siaudypGYM7R+U/BuYXmyHuMkJI2LVJ5Y9dPNKLW3v4xrI1/r9Qy7rPe2r4/rf2opoZYzbHrq+waV5Jm8smmz9t5uChVW19t+6fngasmQmLXa+TG+Clps1Jp3aW43qkYgTlH5j4J5xeaJ++FItd+lFjO2PVT9dba2z8k9pnx7xVCdeTE6q/V0/cpV0dJrbn7s+0cW5Jm8cmmT9t9uKhRU2dN2xrPA1soQlL3SuTyP5W2W6Gm7hpc81T0YK5ReU/DuXGOvJ6Kp9S9HqG8oWun66m1p29KbA1D12arGXPk59/b/ylUT02dpe1m2Tm2JM3k002fVXMQOUVpraXtRniuYyzYrkZNv5q2s82sheubih7MNSLnaTg3zpHXSyLUbyTmnjXObC01z5xrLHfs+iyl4z3b5dqWGpXnD+uryd3SZ7SdY0vSTD7d9EknHC5alNZb2m4UHvI4Pu/F2sXUtK9pO9PsOriOqWjFPCNynobz4hx5rTVGY/5Z48zUUnNLn1KpdYxdnyE31szPfFS+nvp6+o6yc+ydvjpv6Wv8petzTjhc9Cipu6TNDM+1Ta0x26Ta/ilp81TbfoYVNXD9UtGCOXrznYpzK43a/iMx9+j8K9TWPXOuubWMXR8tN06uzh69+Vhba76evqPsHn+HL85Z+ip/7fqcEw4XvVL1754fD4C5Wtg21Cd2PaW2/QwtddfiuqWiBXP05DoV51YSxPuhGG12/hVqaq9pW6tkHXP3R4iNseKzbsnLmp7/7cm30+7xd/nqvKUv8teuTznhcDFKbB6x6ys9D4U1a84+oajR0mek1rpbcJ1SUYN9W/OcjPMqiRi2Y4w0M/cqpbWXtmtVso65+71C+Vd+xqX5Q/Xk/i4RyrvD7vF3+OKcpS/zF6/POOVwMUpsLqFruzzXPFZvDPvV9v9p7TdCT90tuFapqMG+LTlOxnmVRA7bl/arMTP3KqX1l7TpUVJH7n4PfpYnBeuj2LXQ9ZhU/tVG1DAix0pvq1dSH3/x+oSTDhcjheYTurbTc+1bPgP2rc1T236kHWNzjVJRiv1acpyO88pFCfap6VuCeUfmXilXe+5+r5r1K21Xi5/jaRETu5frR7XtZ+mt4ZR51HhbvZL6+avX9UoOMW/GefHvEzw/g9bPgv0ZKaXtRjth3FyUYr/a/qfjvFJRg31bcqTMyrtSqvYVc6sZo7RdCX52oVglN1aoHv79FGofU9N2ttY6TppDrbfWLamdv3pdbcdBaofn/E6e6/PzqP1c2Id5cvlK2oy2Y8wfrksqSrBPbf/TcU6pqMG+LTlSZuVdLVZ/7PpINetX2i6Gn1coVqsZs7TOkjZ/SvOt0FLDKbW3enPtktr5y1eVt20Wb9+ca/zmefp8nwe+ms8n1Z75cu1WSdWyCtckFTlsX9rvLTivWNRi/9Y8ITNy7hCqf9W8asepafuHn1EsdqkZ+9c2VXPq3tMJc3+qreOk2lu9vX5Jbfzlq8qbNosbNucaz4PZ6Z4Hv9LPqbQt87IP/54pNP4OXItUpLBtSZ834bxC0Yp5evP9jM63S2gO/HuG0Lg5pe352aRip9LxQ+1C9YeuhZS2W6GmjpPq7nHDHCS18devam/YNE45WK32tjk/P6dc7SVtiLlDMdOqcUpw3qmIYbuSPm/COYWiFfP05vsZnW+n5xxWzallnFR7fh6hYNudSsYvqfPZprb9CUpqOa3mXjfNRVIdf/2qdvqm8dukT69zhjfO+/l5perP3c/hGL35Sq0apwTnnYoYtsu1fxPOKRQ9mGtGzjd7zmHVfFrXLlRrKkJS91bJjV9bY27Of0rarFRSR0mbN7ltPpLq+ARQtZM3jtMOFju8df7Pzy42h9S9GhynN1/KijFqcN6pCGGbXPs34XwYIzBnb+5ReU6xci49a8e+oUgpabNCqobUvZTUGqTu7ZKq5bRaR7lxTpLK+QRQtZM3jls36xpvXoPn4TA0j9j1FhxnRM6Q2flbce6pIN6PtXsbzocxAnP25h6V5xQr51I7Ftc6FCVq28+SGj91L+c5N86Tf+8Wq+W0Oke6dV6SyvkUUJMTN5CbN+yn3Bzfvg6/+p8RujdKbKxRZubuxbmnorTfm3EujFGYtyf/iBwnWTmXkrG4vqGo1dpvtFANI2oL5ehZr5lYz4k1jnb7/CTl+RRQk9M2kC9s2k+5ud6wHs8DYyhGWpX7RJx7Kkr6vRnnwhiJuXvyj8pzgpXziI3F9cxFjdZ+M7AG/t0iNr+eNZuFdZxU2yy3z09SGZ8EanLSJnLaoWKV1HxvWQ8eGmd+1rPyz8g5GueeipI+b8V5MEZi7p4xRuQ4wco5hNaM10IRy1Gqtv0srIF/twrNL7RO/HuH3/gn1LLKV+YpKc0nwQfMeODPyNkidLD4kti8b1qT52fMGI35R4wxMtdMnHcqcu3fivNgjMb8reP09j/FyjlwzVKRUtLmpzTnCs8aRtYTml/o2m4nfRarfGmuktJ8GnzEjAf/jJw1vriBh4Tmf+PaPOc0c24co3ecUXlW4dxb4q04D8ZozN86Tm//U6yaA9crFKVq2te0na1lriWYc9Y4PU6rZ5UvzllSmE+DDxn98B+dr9ZXN/GQ0DrcuD7Pw+TM+XGM3nFG5VmFc2+JN+IcGDNwjJaxevqeZMUcuFa9Y5b2L2mzysxanrlL12alnfXsGvfPzrElnccnwseM3ARG5qq1cxM/Fdfj1jV6Hipnz2/UWCNyrMa518YbcQ6MWThO7Xit/U4zew5cp1FjleQpabPC7Dqe+WePVWvkZ15rx5g/O8eWdCafCh80ajMYlacGDxf6p+ea7DrozPY8xK2Y44ixevvvwrnXxtuwfsYsHKd2vNZ+J5k9B+YfOU4uV+7+KqPnHTJjfUfYWdOOMZ92jy/pPD4VPmrUhjAqTw437pnjzsy9Atfp7fMJeR7mVsyxd6yevrtx7jXxNqyfMRPHqhmzpc9pZtfPNRo5Tipn6t5qK+qYtcY9dtWzY0zaPb6kM/lk+LARm1Nv/5TUph26NlJs3Lf41f72ecQ8vxur5sjxasZs6XMazr003oS1M2bjeKXj1rY/0cz6uT4zx6DY9dVmzv1n9hq32FXP6vFiTqlD0ll8Mnxc78bY0zempKbc/VFKajnVroPPKs/5rZonxysds7b9qTj3kngT1s6YjePVjNvS5ySzaue6jM7/E8o9e8waK+rIzTd2fZZcPbOsHi/mlDoknceng/6/1o2itR/VbtSl7UZZPd4otev6Ns/5rZojxywZt6bt6Tj3kngL1s1YgWOWjl3b/jQzaueajMwdwjH49y6r6kitc+jabLFaZlo9XspJtUg6i08H/Z/WzaK135+WDbq2/SgttZ7grXWX+M3tGStwzNy4pe3egnPPxVuwbsYqHLdk/Jq2JxpdO9djVN6U5zirxiyxopbUOoeuzRarZabV46WcVIuk8/iE0D+0bBqtfVr6/WntN0pP7Tu8rd5av/k9Y5WacUvbvQXnnos3YM2MVThuyfg1bU8zunbmG5GzxHOsleOmrKojttb8e4VQHTOtHq/EafVIOotPCP1L7cZR2j52QKjV23+UkXWMWpuYmblP8Fy/1fMsHbukzRtx/qk4HetlrMSxczWUtjvRyLq5DiNy1tg1bsjKWkJjrRiXQnXMtGqcGifWJOksPiUUVLOB5NqO3IxH5hphRj3PA8yo/CNznYjrtXqeHDs0fure23HuqTgZa2WsxvFTNZS2O9GourkGI3LW2jVuyKo6Quu9YlxiDbOtGqfWiXWt/mwkpflLVFTNgzrUdsbDfnS+UWbM9em5ebaM9exT2/ctetZnBI7PGmLXb8G5x+JkrJWxGsdP1VHS5lQj6ub8e/O12jn208o6ONaKMYk1zLZqnFon1PX8LFZ+JpLK+atUUumD+7nxz3zgz8o7ysr6uMGm1p33Y+3ejOuwY44c/1lD6NptOPdYnIp1MnZgDbFacvdP1ls3596Tq9fu8X9W1rB73VePvWqcFqtr42e/enxJbfylHubEh2dJTase/CvG6LVqLWK4Gf9qYV07a5yF894xR47P9d9R00qceyxOxBoZO7CGWC25+yfrqZvzbs0zytdq2L3uK8deNU6r2bXxs549nqR5/PUe6MSHaqim1RvBijFGWrUuJfhZ/eo6qcZRQvPcgXWcUNMqnG8sTsP6GLuwjlg9ufsn6qmX823NM8oJNfxZWcPOOa8ce8UYvUbW+FzbVWssaR1/0Yc68WH7qym2GYSujTQ7/yyn1M3PjZv7KXX24px2zot17K5nFc43FSdhbYydWEuoptS9U/XUy/m25BjphDpWj79zzrPH3Tm3Wr01Puf6ljlLaucv/GCnPYBzm0Lq3giz88+UW7tVQnVw0+f9NzppPqzlhJpW4HxjcRLWxtiJtYRqSt07VWu9nGtt/xlOqGX1+LvmPGNMfp8YJ6upj/Oq6SvpDv7qD3fCg5kbBP9+Xp9pdv4Vdm+4qbFvOhBwLrvnw1p217MK5xyLU7Auxm6sh3XFrp+spV7Os6bvTLvrWT32rvmOGpffIQbxfqzdaqkaWGuqraTv8EnwAic+sEMbCf8eaWbuWbjppmKVkvF21TYa57F7Lqxldz2rcM6xOAFrYpyANT1rC107XW29nGNpvxV21rR67F2fQc+YrJnRinl6ctV6jscaVtYh6V18OrzEqQ9y1sW/R5mVtwQ31JpIYdtc+1FKx9pR22inzeG0elbhvGOxG+thnIA1PWsLXTtdTb2cX0mflXbWtXLc3zir51s7Hr8rjJk41ugxmXdkbkn384nxIqc+4J91zapxVt4fbqSMmTjW7DFr86+qawbWvrv+k2pZifOOxW6sh3EK1hWL09XUyrmV9FltV20rx/2NsXLMPyXjPduE4gSsqaWunr4znVaPpDh/rS9y8sP1V9uMGmfkPBUPBjM2+dacM2ua6bS6T6tnFc47FjuxFsZJWFsoTldaK+eVa7/LrvpWjfkcY+VcY2PxO8F4C9adqj93f4fT6pGU5y/2ZU5+yM7aBGbkfAMeBkaub2uuGbXMxpp3131SLatx7rHYhXUwTsLaQnG6klo5p1z7nXbUN3u82Jxi10fj556K23Bu/PsEPbX09JXUx1/fC5380JyxOY3O90Y86PSuSW+OkbWswHp31sw6dtayA+ceix1YA+M0rC8UJ8vVybmk2u62q8YZ43EunFfo2gwch/ElJ867tZbT5iF9kb/Alzr14TljkxqZ6+14AGpd69Z+1FvHSifVelItq3HusdiBNTBOxBoZJ0vVyXnE2p1iR40jx+M6x+bDe7w/AvPPGucNTpx/Tz2t/SSN5S/xxU59kPZsDjQqz414OKpZ99r2OS01rMYad9bJOnbWsgPnHovVOD7jRKyRcbJYnZxDqM1pVtc5Yjyub2lOtmPfXP8U5unJ9XYnrkFrLafNQ/o6f40vd+oDddTDfkSOL+CBqWTdStvVqK1htZPqO6mWHTj/WKzEsRmnYp1vqzl2PdbmRKtrbR2L61pbd2kftku1/cO2JX1udtoa9NTS2k/SPP4qL3Diw3XU5tXb/2t4eEp9Bql7PTj2jDFasa6dtbGOnbXswvnHYhWOyzgZaz295liNrJ/3T7Wy3tqxuJ61/Z9G9X3m4LWW3Dc5bR1a6zhpDpL+yV/mJU58yPY+/Hv7fx0PVFxP/j1abNzdWNfO2k6pYxfOPxarcFzGyVjr6XWH6mPdp9YesrLmknG4jqPqG5XnD+salffNTluH1jpOmoOkf/PXeZHTHra9G1lrP/0bD1i/te35fEqFxt3tlJpOqWMnrkEsVuCYjNOx3pPrZn2s+dS6Y1bVnRqH65dq22pUTtb3zBe6drvT5txTS2s/Sev4K73MaQ9eN5GzPA8ZjNk4HmMljr16/KdT6tiJaxCL2Tge43Ss9+TaWR/jbVbVzjG4bjPrGJGbNfbkusVpa9Fax0lzkJTmL/VCpz2AWzeFlj4qt/oQxvFKYiaONXu8mBNqOAHXIRYzcSzGG7DmU2tnfSfXWmJF/VynUMzUMw7rbM1zm5PWoqeO1n6S9vAXe6mTHsYtG1xNW7WbfRhj/lExAnOOyluLNeyqYzeuQSxm4liMN2DNJ9bO2k6ts8bsOXCdZo8X0jom663tf6uT1qO1hlPql1THX+3FTnoo124SNW3VZ/TBjPlK8rJtS7RgjtY8vU6o4QRch1jMwnEYb8CaT6yfdZ1WX63Zc+A6zRonpWVs1lzb/1YnrUdPDa39JO3nr/dyJz2gazaa0nYaY8SBhDl6cv0wV0vk1LafgTXsquMEXIdYzMAxGG/Buk+qnzWdVl+LmXM4ZY1qa2Ddpf1ud9J6tNZwSv2S2vkL/oBTHtQ1G19JG43Vclhjn5q+rThWS+Ty7XBCDafgWsRiNOZnvAXrPql+1nRSba1mzeOkNSqtgzWX9PmKk9ajtYbWfpLO4i/5I055aJdsfrzPvzVP6aGN7VJtV2E9vbEax99Rwym4DqkYibkZb8G6T5oD6zmhpl4z5nLSGpXWwnaptl9zypq01tDaT9KZ/DV/xEkP7txGErqX66NxngeV55rzOu+fivXWxko7xz4N1yIWIzE3401Y+wlzYC276xll9HxOW6NcLaw31faLTlmT1vFb+0k6l7/qDznlId66Gbb0eYuTDk6sJRRvx/mUxAo7xjwZ1yMWozAv401Y+wnzYB07axlp5HxOXJ9UPaw31OarTlmX1vFb+0k6n7/sjznlYd6zsbT2exMeHBizcbwVY+7EuaZittXjnY7rEYsRmJPxNqx/5zxYw85aRhs1nxPXJlYTr8cf4dYAACPpSURBVPP+152yJq3jn1C7pHn8dX/QCQ/13s2xp+8NeOhitGAOxhdwzrGYaeVYb8E1iUUv5mO8DevfOQ/WsKuOGUbM6dS1CdXEWk+q9wSnrEvr+K39JL2Hv/KPOuEB37tB9va/GQ9njFy72P2v4LxjMQPHmDXOm3A9YtGL+Rhvw/p3zoXj76hhlt45nbwurC0U+q+d69L7ubT268W6e+YgqYy/rg874eE64iHf2/+LuMmm1rC03Y0491iMNjv/G3FNYtGDuRhvxDnsmAvH3lHDTD1zOn1NWN/Jte62Ym34GZRGTkmbHI5ZGpLW85f3cbsfwKM2gRE5vqZmzb68YXPuqRiFeUfmfjOuSSxaMQ/jjTiHHfPhuCvHnq1nTqevCes7udadZqwNc5ZECtvGorY9Q9I7+Gv9GD6sGTuMGntUni9oWacTvis7cf6xGGVW3rfjusSiBXMw3orzWD0fjrty7Nla53T6erC+U+vcrWdtuLYl0Yv5WkPSu/krvgAfzKmIYbtU2xlGjjkqz61a12fn9+MkXIdY9GK+ETlvwDWJRQvmYLwV57FyPhxz5dgrtMzpDWvBGk+tc6fSteE6lsRozN87BnONyClpHX+th+JDNRUjMffo/DGjxxuZ6xYj1mTHd+NUXItY9BiZ6yZcl1jUYn/GW3EeK+fE8VaMuVLtvN6wFqzx1Dp3Ca0Nr5XEChxz1biSzuaTYCE+hFOxG+tZUdfoMUbne7OR67DyO3E6rkUqWozIcSuuTSxqsC/jzTiXVXPieCvGXKlmXm9YB9Z4ap07cF1KYwfWsKsOSWfyiTABH7pvf/hyHjPnMiP/6HxvM2P+q74Pb8H1iEWLETluxbWJRSn2Y7wZ57JiXhxn9ng7lM7rDWvAGk+tczWuSShOwbpOqk3SOXwyqBg3lRkby6zcM3KebvacZ38X3ohrEosaPX1vx7WJRSn2Y7wZ57JiXhxn5li7lMztLWvAOk+udQWuxcnrcnp9ks7iU0LVuNGM3nBG5/uZlfdEq+Y56zvwdlyXWJRgn9J+X8G1iUUJ9mG8Hecze14cZ+ZYu+Tm9pb5s86Ta52N63DqmrC20+qTdC6fFurCzWfUBjQyF83Ke4rV8xv92d+Ev41Y5NS2/xquTyxy2J7xdpzPzLkx/6xxdkvN7S1zZ50n1zoL5884CWs7rT5J5/OpoSG4GfVuSKPyxMzMvcuuOY383G/E9YlFCtvm2n8R1ycWKWzLuAHnNGtuzD9jjBPE5veWubPOk2udgXNnnIS1nVafpPfw6aHhuEG1blI9fUvMzr/S7nmM+LxvxzWKRUxpu6/i+sQihW0ZN+CcZs2N+WeMsVtsbm+aN2s9vd5ROOeT58/6TqxR0rv4FNE03LBqN63WfrVm55/tlPp7Pusv4TrFgng/1ObruD6xiGE7xg04pxnzY96RuU8Smt+b5s1aT693BM735LmzvhNrlPROPk00HTewmk2stn2rVeOMdGLNrZ/zF3GtYpHqo3/jGsUihG0Yt+C8Rs+PeUfmPgnn96Y5s9bT6+3FuZ48b9Z3Yo2S3s2nipbiplaysZW261Vb104n1/emddyNaxWLWHuFcZ1iQbzPuAXnNXKOzDcq74k4x7fMl7WeXm8rzpFxmtPrk3QPnzDaghtdarMraVOC47XECU6pI+XEdTsZ1ysWobb6N65RKmr63YRzGzVH5huR81Sc51vmy3rfUHMNzo1xEtZ2Wn2S7uSTRltx43tugLzWG7XYPxUrrBxrhNXrcwN+r0pCYVynWNT0uQnnNmqOzDci56k4zzfMlfW+oeZSnNfJc2R9J9Yo6V4+cbQUN7xchPruxPpSMdLofCvMXI/bce1yoTCuUyxK29+EcxsxT+bpzXcyzvEN82S9b6i5BOd08vxY34k1SrqfTx4dh5vjb4Pk3ydhvan4ki/PvRfXLhcK4zrFoqTtbTi/3nkyT0+u071tnqz3DTXncD4nz431nVijpO/wCaSjccN808bJmlNxsy/NdQauXyoUxnVqjdtwfr1zZY7WPG/wtnmy3jfUHMI5ME7D+k6sUdL3+CTSK3ADffNGyjmk4ha3zmslrmEs9G9co9a4DefXM1f2b83zBpzj6fNkrafXG8L6GadhfSfWKOm7fCLpVbih3rKpck6peCvO481z2YlryFAY16klbsQ5ts6V/VtyvMWb5slaT6+XWPvp83hDjZLk00mvww325o2Wc7w1VIfrx1AY16k2bsQ5ts6XfWv7v8lb5sk6T66VWPfqOXDM2pCkk/mU0mtxw/3Kpss53xYqw3VjKIzrVBO34jxr58t+tf3fhHM8eZ6s8+Raf1hva+3suzIk6XTHPKl8aKoFN97bN2DO8+ZQHteMoX/jGtXErTjP2vmyX03ft3nLPFnnqbWyxptCkk511BPKh6ZaceO97XvEub15fpxHLpTG9WLo37hGpXErzrN2zuxT2u+N3jBP1nhSnazr1OgxMpckzXDkk8kHplpw073he8T53DCnH84rF4rjWjH0b1yjkrgZ51o6Z7Yv7fdGnOOJ82R9u2tkLaviBCfWJEl/jn0i+cBUK266b/wesf43zqEU55kLhXGdXLM8rlMubsa5ls6bbXPt3+wN82SNq+vk2C1xm9vnJ+l9jn8S+bBUC264b/kesea31D0C550L/RPXh6F/4xrl4nacb8m82TbX/s1OnyfrW1Ejx6uNL/ny3CWd5RVPIB+WasUN99Tv0RtqXIVrkQv9F9eGoX/jGqXidpxvbt5sl2r7dpznaXNlbbPq4xi1oX+voSSt9qonjw9LteBme9J36NS6TsH1SYX+g+vC0L9xjVJxM841N2+2ibW7wcnzZG0j62Pe2lCcayVpl1c+cXxQqhY32p0bLmvYVcebcL1Sofx66d+4RrG4Hecbmzfvx9rd4uR5srae+pinNlTPNZS02mufND4o1YIb7crvEMddOfYtuH6p+DquB0P/xPWJxe0439jceY/3b8J5njRX1lVbG/vWhsZxbSWt8vonjA9J1eImO3uz5Tgzx/oKrmcqvoxrwdA/cX1CcTvONzZ33uP9m5w6T9ZVUhvb14bmc80lzXbFk8WHpFpwkx39HWLu0fkVXuNYfBXXwTWJ4/qE4gs4Z86d13n/NifOkzXF6mKb2tA+fhaSZrnqieIDUrW4wY74DjHfiJxK43qn4ms4f4b+i2sTii/gnDl/Xrt9XU6cK2tKfTY1ofP4GUka7boniQ9IteAG2/IdYv+WHOrD9c/FV3DeDP0H1yUWX8A5P+fOazevyYnzZE09offws5M0yrVPEB+OqsXNtfQ7xD6l/TQPP49cfAHnzNB/cF1C8QWccy5uddI8WUtL6P38TCX1uvrJ4cNRLbi5xr5DJW20Fz+jXNyO82Uov0ZfWSfOORU3O2WurKM0dC8/a0mtPvHE8MGoWtxYn9+h2HWdi59ZLm7GuTK+jusRiq/gvGNxqxPmyRpyoe/xOyCp1meeFD4YVYubKkPvw88wF7fiPL8w51Jcj1B8Becdi1vtnifHD4X043dDUqnPPSF8MKoWN1W/P+/HzzMXt+H8GF/GtYjFV3DejJvtmivHDYUUw++K3xdJ9Nmngg9ExYQ2Tl5zU70HP9NU3IRzY3wZ1yIUX8F5M261Y54cMxZSied3hd8hhqRv+fSv3gef/qQ2Ql5jW7bXe/FzTcUtOC/GV3EdQvEVnDfjVqvnyfFCIdUq/d7wu+b3Trqbv+z/KX9A6g6lm1vsHvvH2umd+NmWxJtxLowv4hqE4ks49y+sw6p5cpxYSK16vz/8Lvq9lN7PX+//8oF2r5YNq6Qd85b00Xvws62Jt2H9jK/h/EPxJZz77euwYo4cIxbSCLO+T/y+MiSdaemvkw+G00Pv1Ps51vThWLHQe/GzrI23YN1vnMMonH8ovoRzv30dZs+R+UMhzbD6u+X3WjqTv8YAPrB8aJ1t1GfV0p9j14bOws9nRpyKdTK+hHOPxVdw3revwaw5Mm8spJn8jknyKZDATdmH5hlmfCaluTj2rNA8XOvdcRLWxvgSzj0UX8F537wGs+bHvKGQVvH7Jn2bT4AC3KTdrNeave6pnBx7d6gc1+4tsRvrYXwF5x2Kr+C8GTcZPTfmi4W0mt876bv89Vfipu0DdI5V6xvKz8/3DfFVXIcbYwfWwPgCzjkUX8K537oOo+bGPLGQdvI7KH2Tv/xG3MTdzN/n93nxM6yNEuyzMm7AOX05VuG4jNtxvqH4Es79xnUYNS/mCYV0Cr+P0vf4qx+AG7sP07Pxs6qNkZh7ZZyINZ4SNdh3ZszG8Rg341xj8RWc941r0Dsv9o+FdBq/l9K3+IsfiJu8D9Qz8DOpjR1Yw8qYjeOdFDNwjJkxA8eYPd5JON9QfAXnfeMa9MyLfUMhnczvqfQd/tIn4cbvQ3UdrnttnIy1roxa7H9S7MI6ZscIzMm4Gecaiq/gvG9bA86pdF7sEwrpTfzOSvfzVz4ZDwI+WMfj+tbGDTgn4x2fK2ueHa2Yh3ErzjMUX8F5M96udj5sHwvpjfzuSnfzF74IDwUeDtpxDWvjSzj3G+MmnNvsqMG+jBtxjqH4Es79pnWomQ/bhkJ6O7/H0r38dW/Ag4IP2TyuV23on7g+p8dXcR1mRw7bM27D+cXiKzjvW9aAc4nNh21iId3C77N0J3/ZG/HQ4IP2v7guLaF6XMPVoTSu18yIYTvGbTi/UHwF533LGpTMhW1CId3I77Z0H3/Vh+BB4msPXM69NphLY3G9e0NjcF1nRum4t+H8QvEVnPcta5CaC++FQrqd33PpLv6iD8ODRelDt6btCTjH2ghJ3VM7rn1paC2u/864CecWiq/gvG9YA87jNxdei4X0FX7fpXv4az4UDxmlh41YO+Z5W+SUtlM5fgax0Jn4Oe2IG3BOofgSzv3t6xCaA6+FQvoiv//SHfwVvwAPHl+IGrXtlcbPIhR6H36Gq+LtOJ9QfAnn/vZ14BxKQvo6fwfSu/kLfgkeQG6LVj199U/8TEKhe/CznR1vxXnE4is47zevAevPhaT/8jchvZe/3sPxANIazLUCa2D0GpFD+c/Jdf4GfuYz4q04j1B8Bef95jVg/bGQFObvQ3onf7mH4gFk9EN2Rs4f1j16DiNzfRk/m1Dou/hdGBVvxDmE4is477euAWuPhaQ0fyfS+/irPQwPH7MfrKPGYc2MUUbm+ip+NqGQnvj96I23Yf2h+ArO+41rwLpDIUnSrdzlDsHDx+oDSOu4rLk1T4kZOb+En08opBL83rTGW7DuUHwJ5/6mdWC9oZAk6WbudJvx4HHC4aOkDtZ8Uv36J34+oZB68PtUE2/AmmPxFZz3W9aAtTIkSfoCd7xN3nDwCNXHukNtdAZ+PqGQRuN3rCTegDWH4is47zesAetkSJL0Fe56i7310MG63ziHr+DnEwppJn7fSuNkrDUUX8F5v2ENWOcbapYkaQZ3vkXeeuBg3W+cw1fw8wmFtBK/fyVxKtYZiq/gvE9fA9bIkCTpS9z5JuIh4y0HDdbMiLXTHvwcQiHtwu9iaZyG9YXiKzhvxklYG0OSpK9x95uAB4y3HDJYc65+tgmF5uFah0I6Ab+XpXES1haKL+HcT1wH1sWQJOmL3AEH4uHiLQcM1sz6eS02N94PhfpxTUMhnYjf05I4BeuKxVdw3qetAWtiSJL0Ve6CA/Bg8ZbDBWuORQ/mYqgc1y4U0un4nS2NE7CmUHwF533SGrAehiRJX+ZO2IGHijccLFgvYzaOFwr9E9cnFNKb8PtbGruxnlB8Bed9yhqwFoYkSV/nbtiAB4oTDxWsLxe7sI5QfBXXIRTSm/H7XBI7sZZQfAXnfcoasJZT6pIk6RTuiBVOPkzEauN1xolYI+N2nG8opFvwu10aO7CGUHwF583YgTUwJEmS/wBQ5I2HCNb8tvqfWH8obsA5hUK6Fb/rJbEax4/FV3DeO9eA4zMkSdJ/uCsmvOUAwTpjcQvOKxStmOeUkL6A3/uSWI3jh+IrOO9da8CxGZIk6b/cGYEHh9MOD6ytJL6Ac74lpK/hb6A0VuG4ofgKznvHGnBchiRJ+id3Rzjp4MCDTCpCfb6Ka/PGkL6Ov4mSWIFjhuIrOO/Va8AxGZIk6d8+v0PywLDj0MDxU5FS2u5GXKfWWG33+NLJ+Psoidk4Xii+gvNeuQYcjyFJksI+uUumDgmhayPxkJKKGq393opr9db5v7VuaRX+vktjFo4Ti6/gvFetAcdiSJKksKt2SR4AYhGTuleLY6ai18hcJ+O6vX3eN8xBWoW/l5KYheOE4is47xVrwHEYkiQp7tqdMnQY4CGhNmLYLhWjleYubXcart9b50E3zUVahb+b0hiN+UPxFZz37DXgGAxJkpR2zW7Zcwgobc8xUrFC63istbb/TKzrxBp73TovaQX+fkpjJOYOxVdw3jPXgPkZkiQp79U75qiNf3f/FqPm/sOD1Ki8JTjujhpWuX1+0ir8LZXEKMwbiq/gvGetAXMzJElSmVftmjM2/J48I+uoMXoNYrjeI8dj3hljnOYr85RW4W+qNHoxXyi+gvOesQbMy5AkSeWO3zlnbvI9OXv69pi5HiV48Kqpg/1q+7/ZF+csrcLfV0n0YK5YfAXnPXoNmHN0fkmSvuS43XPV5t6Tu6dvjxXr0oKf2a8+XuP9L/n6/KXZ+BsriR7MFYqv4LxHrgHzMSRJUp1jds/Vm3nLWKtrfHrbgYeHtLfUPYPrIK3B31pptGCOUHwF5z1qDZiLIUmS6n1yB205OOw8cLz1wPO2emfwwCqtx99dSdRi/1B8Bec9Yg2YhyFJktp8bhdtOTi09BnlrQeet9U7gwdWaR/+/kqiBvuG4is47941YA6GJElq96mdtOXg0NJnlLceeN5W7wweWKX9+DssjRLsE4sv4JwZNdiXIUmS+nxqN605POw+bLz1wPO2emfwwCqdhb/JkijBPqH4Cs67ZQ3YjyFJkvp9ZketOTzUtJ3hjQeet9U7k4dW6Tz8XZZGCtuG4is475Y1YL+WHJIkKe0Tu2rN4aGm7QxvPPC8qdbZPLRK5+LvszRi2C4UX8F5164B+zAkSdIY1++qNQeHmrYzvPGw86ZaZ/PAKr0Df6slEcI2ofgKzrtmDdieIUmSxrl+Zy05PJxwyHjjYedNtc7mgVV6F/5mS6M2x1dw3qVrwLYMSZI01tW7a8nhoaTNbG887Lyp1tk8sErvxN9uadT2/wLOmRHCNgxJkjTetTtsyeGhpM1sbzzsvKnW2TywSu/H33FJ1PT9Cs47tQa8z5AkSXNcucvmDg+nHDDeeNh5U60rvPEzlPRvfAEdGV/BecfWgPcYkiRpnit32tQB4pQDxil11HhbvbN5aJXuw9/1iPgKzju2BrwXaydJksa7brdNHSBS91Z560HnbfXO5qFVuhd/373xFZx3aA14nSFJkua6ardNHR5S92aKHW521dPiTbWuEPtMJd2Dv/Pe+ALOmfPnNYYkSZrvmh03dnhYfbAoOdDErp8mNYevKvl8Jd2Dv/nW+ArOuzQkSdIa1+y6oQNE6NpIPMCUjlfabqc31Lhay2ct6f3422+Jr+C8S0KSJK1zxc4bOkCErvUacWhp7bfSG2pcbcRnL+m9+Ayoja/gvHMhSZLWcveN4CFl1EFlVJ5ZTq9vlxnfBUnvw2dBaXwF550KSZK0njvw/1pxMJmVd5TT69tlxXdD0nvwmVAaX8A5p0KSJK332R14x0Fk1TgtTq5tpx3fE0nn47OhNG7H+cZCkiTt8aldeOfhY8eY6uOBVVIOnxO5uB3nGwpJkrSPO/EiHnrexQOrpFJ8XuTiVpxnLCRJ0j7uxIt46HkPD6uSavG5kYpbcZ6xkCRJ+7gTL+CB5108rEqqxedGLm7EOYZCkiTt5W68gIee9/CwKqkFnx25uBHnGApJkrSXu/FkHnjew4OqpB58huTiJpxbLCRJ0l7uxpN54HkHD6mSRuCzJBU34dxCIUmS9nNHnsgDzzt4SJU0Cp8nubgF5xUKSZK0nzvyRB54zsbDqYdUSSPwmZKKG3BOsZAkSfu5I0/iYedsPJR6QJU0Cl98c/F2nE8oJEnSGdyVJ/HAc6bYoZR/S1IPPmtS8XacTygkSdIZ3JUn8LBzptRhNHZdklrwBTgXb8V5xEKSJJ3BXXkCDztnKTmIpu5JUgs+e1LxVpxHKCRJ0jncmSfwwHOOkkNo7r4kteCLcC7eiHMIhSRJOoc782Aeds5QcwAtaSNJLfgsSsXbsP5YSJKkc7gzD+ZhZ7/ag2dNW0mqwZfhXLwJaw+FJEk6i7vzQB529mo9eNa2l6QafDal4k1YeygkSdJZ3J0H8rCzT+uBs6WPJNXgS3Eu3oA1x0KSJJ3F3XkQDzp79B42W/tJUg0+q1LxBqw5FpIk6SzuzoN40FlvxCGzt78kleCLcS5Ox3pDIUmSzuMOPYAHnbVGHjJH5JCkEnx2peJkrDUWkiTpPO7QA3jQWWfk4XJUHkkqxZfkVJyKdcZCkiSdxx1arzDjYDkylySV4LMsFadinaGQJElncpfW8WYdKmfklKQcviyn4jSsLxaSJOlM7tI61uwD5ay8kpTCZ1sqTsP6YiFJks7kLq0jzT5IzswtSTl8YU7FSVhbKCRJ0rncqXWUVQfJ2fklKYXPulSchLWFQpIkncudWsdYeYBcNY4kxfDFORUnYE2xkCRJ53Kn1nY7Do8rx5KkED77UnEC1hQKSZJ0NndrLRc6MK48OHpQlXQKPg9TsRvrCYUkSTqbu7WmKzkgxq7PkKpDklbi8zEVO7GWWEiSpLO5W2u42gNhSZuRSuuSpBX4zEzFLqwjFJIk6Xzu2OrCA2DLIbClT4/WOiVpBj5DU7EL6wiFJEk6nzu2qow+8I3IUWNU3ZI0Ep+tqViN48dCkiSdzx1bSbMPeDNypsyahyT14LM2Fatx/FBIkqR3cNfWP6w81M3OH7JiXpLUgs/fVKzEsUMhSZLewV1b2w5xq8f7s2OeklSCL9WpWIXjxkKSJL2Du7a22HFg9KAq6XR8sU7FChwzFJIk6T3cubXFjkOjh1VJp+PLdSpW4JihkCRJ7+HOreV2HRg9rEp6A75gp2ImjhULSZL0Hu7cWm7XgdHDqqQ34At2KmbiWLGQJEnv4c6tpXYdFj2oSnoTvmSnYhaOEwpJkvQu7t5aateB0cOqpDfhi3YuRmP+WEiSpHdx99YyOw+LHlYlvQ1ftlMxGvPHQpIkvYu7t5bZeVj0sCrpbfiynYuRmDsUkiTpfdzBtcTOw6KHVUlvxZfuVIzE3KGQJEnv4w6uJXYeFj2sSnorvnTnYgTmjIUkSXofd3BNt/ug6GFV0pvxxTsVIzBnKCRJ0ju5i2u63YfF3/i765CkFnz5zkUv5guFJEl6J3dxTbX7oPgcf3ctktSKL+Cp6MFcsZAkSe/kLq6pdh4UOTb/lqS34At4LloxTygkSdJ7uZNrmt0HRY7PvyXpTfginopWzBMKSZL0Xu7kmmbnQTE2duy6JJ2OL+K5qMX+sZAkSe/lTq4pdh4SU2On7knS6fgynopa7B8KSZL0bu7mmmLnQTE1duqeJJ2OL+S5qMG+oZAkSe/mbq7hdh4SS8YuaSNJp+JLeSpKsV8sJEnSu7mba7hdh8TScUvbSdKJ+FKeixLsEwpJkvR+7ugaauchsXTs0naSdCq+nKeiBPuEQpIkvZ87uq5QczitaStJJ+LLeS5S2DYWkiTp/dzR9XotB9OWPpJ0Er6gpyKFbWMhSZLezx1dr9dyMG3pI0mn4Ut6KmLYLhSSJOkO7up6tdaDaWs/SToJX9RTEcI2sZAkSXdwV9ertR5MPdRKugVf1lNBvB8LSZJ0B3d1vVbvobS3vySdgC/rqSDeD4UkSbqHO7teacShdEQOSToBX9pTUdtPkiTdw51drzTiUDoihySdgC/tqajtI0mS7uHOrtcZeSAdmUuSduKLeypK20uSpLu4u+tVRh9IR+eTpF348p6K0vaSJOku7u56ldEH0tH5JGknvsD3hiRJuou7u15jxmF0Rk5J2oUv8D0hSZLu4w6vV5h5GJ2ZW5JW44t8a0iSpPu4w+sVZh5GZ+aWpNX4It8akiTpPu7wOt7sg+js/JK0Gl/ma0OSJN3JXV5HW3UQXTWOJK3AF/rakCRJd3KX19FWHURXjSNJq/ClviYkSdKd3OV1rJWH0JVjSdIKfKkvDUmSdC93eul//AcASXfiy31JSJKke7nTS//Lg6+k2/DlviQkSdK93Oml/+XBV9KN+IKfC0mSdC93ekmSLsYX/FxIkqR7udNLknQxvuDnQpIk3cudXpKki/EFvyQkSdKd3OUlSboYX+5LQpIk3cldXpKki/HlPheSJOle7vSSJF2ML/i5kCRJ93KnlyTpYnzBz4UkSbqXO70kSRfjC34uJEnSvdzpJUm6GF/wcyFJku7lTi9J0sX4gp8LSZJ0L3d6SZIuxhf8XEiSpHu500uSdDG+4OdCkiTdy51ekqSL8QU/F5Ik6V7u9JIkXYwv+LmQJEn3cqeXJOlifMHPhSRJupc7vSRJF+MLfi4kSdK93OklSboYX/BzIUmS7uVOL0nSxfiCnwtJknQvd3pJki7GF/xcSJKke7nTS5J0Mb7g50KSJN3LnV6SpIvxBT8XkiTpXu70kiRdjC/4uZAkSfdyp5ck6WJ8wc+FJEm6lzu9JEkX4wt+LiRJ0r3c6SVJuhhf8HMhSZLu5U4vSdLF+IKfC0mSdC93ekmSLsYX/FxIkqR7udNLknQxvuDnQpIk3cudXpKki/EFPxeSJOle7vSSJF2ML/i5kCRJ93KnlyTpYnzBz4UkSbqXO70kSRfjC34uJEnSvdzpJUm6GF/wcyFJku7lTi9J0sX4gp8LSZJ0L3d6SZIuxhf8XEiSpHu500uSdDG+4OdCkiTdy51ekqSL8QU/F5Ik6V7u9JIkXYwv+LmQJEn3cqeXJOlifMHPhSRJupc7vSRJF+MLfi4kSdK93OklSboYX/BzIUmS7uVOL0nSxfiCnwtJknQvd3pJki7GF/xcSJKke7nTS5J0Mb7g50KSJN3LnV6SpIvxBT8XkiTpXu70kiRdjC/4uZAkSfdyp5ck6WJ8wc+FJEm6lzu9JEkX4wt+LiRJ0r3c6SVJuhhf8HMhSZLu5U4vSdLF+IKfC0mSdC93ekmSLsYX/FxIkqR7udNLknQxvuDnQpIk3cudXpKki/EFPxeSJOle7vSSJF2ML/i5kCRJ93KnlyTpYnzBz4UkSbqXO70kSRfjC34uJEnSvdzpJUm6GF/wcyFJku7lTi9J0sX4gp8LSZJ0L3d6SZIuxhf8XEiSpHu500uSdDG+4OdCkiTdy51ekqSL8QU/F5Ik6V7u9JIkXYwv+LmQJEn3cqeXJOlifMHPhSRJupc7vSRJF+MLfi4kSdK93OklSboYX/BzIUmS7uVOL0nSxfiCnwtJknQvd3pJki7GF/xcSJKke7nTS5J0Mb7g50KSJN3LnV6SpIvxBT8XkiTpXu70kiRdjC/4uZAkSfdyp5ck6WJ8wc+FJEm6lzu9JEkX4wt+LiRJ0r3c6SVJuhhf8HMhSZLu5U4vSdLF+IKfC0mSdC93ekmSLsYX/FxIkqR7udNLknQxvuDnQpIk3cudXpKki/EFPxeSJOle7vSSJF2ML/i5kCRJ93KnlyTpYnzBz4UkSbqXO70kSRfjC34uJEnSvdzpJUm6GF/wcyFJku7lTi9J0sX4gp8LSZJ0L3d6SZIuxhf8XEiSpHu500uSdDG+4OdCkiTdy51ekqSL8QU/F5Ik6V7u9JIkXYwv+LmQJEn3cqeXJOlifMHPhSRJupc7vSRJF+MLfi4kSdK93OklSboYX/BzIUmS7uVOL0nSxfiCnwtJknQvd3pJki7GF/xcSJKke7nTS5J0Mb7g50KSJN3LnV6SpIvxBT8XkiTpXu70kiRdjC/4uZAkSfdyp5ck6WJ8wc+FJEm6lzu9JEkX4wt+LiRJ0r3c6SVJuhhf8HMhSZLu5U4vSdLF+IKfC0mSdC93ekmSLsYX/FxIkqR7udNLknQxvuDnQpIk3cudXpKki/EFPxeSJOle7vSSJF2ML/i5kCRJ93KnlyTpYnzBz4UkSbqXO70kSRfjC34uJEnSvdzpJUm6GF/wcyFJku7lTi9J0sX4gp8LSZJ0L3d6SZIuxhf8XEiSpHu500uSJEmS9AH+A4AkSZIkSR/gPwBIkiRJkvQB/gOAJEmSJEkf4D8ASJIkSZL0Af4DgCRJkiRJH/D/AIyLBFzXdyxBAAAAAElFTkSuQmCC",
      "text/plain": [
       "BufferedImage@86567ff: type = 2 DirectColorModel: rmask=ff0000 gmask=ff00 bmask=ff amask=ff000000 IntegerInterleavedRaster: width = 1024 height = 1024 #Bands = 4 xOff = 0 yOff = 0 dataOffset[0] 0"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import java.util.Random;\n",
    "class RandomTree {\n",
    "    \n",
    "    static Random random = new Random();\n",
    "    \n",
    "    static void randomTree(double length, double minLength, int thickness, int minThickness, double minAngle, double maxAngle, double minShrink, double maxShrink) {\n",
    "        if (length < minLength || thickness < minThickness) {\n",
    "            return;\n",
    "        } else {\n",
    "             double angle1 = minAngle + random.nextDouble() * (maxAngle - minAngle);\n",
    "             double angle2 = minAngle + random.nextDouble() * (maxAngle - minAngle);\n",
    "             double shrink1 = minShrink + random.nextDouble() * (maxShrink - minShrink);\n",
    "             double shrink2 = minShrink + random.nextDouble() * (maxShrink - minShrink);\n",
    "             penSize(thickness);\n",
    "             forward(length);\n",
    "             turnRight(angle1);\n",
    "             randomTree(length*shrink1, minLength, (int) (thickness * shrink1),  minThickness, minAngle, maxAngle, minShrink, maxShrink);\n",
    "             turnLeft(angle1 + angle2);         \n",
    "             randomTree(length*shrink2, minLength, (int) (thickness * shrink2), minThickness, minAngle, maxAngle, minShrink, maxShrink);\n",
    "             turnRight(angle2);\n",
    "             penSize(thickness);\n",
    "             backward(length);\n",
    "  \n",
    "        }\n",
    "    }\n",
    "    \n",
    "    static void drawTree(double length, double minLength, int thickness, int minThickness, double minAngle, double maxAngle, double minShrink, double maxShrink) {\n",
    "        clear();\n",
    "        reset();\n",
    "        penUp();\n",
    "        turnRight(180);\n",
    "        forward(100);\n",
    "        turnRight(180);\n",
    "        penColor(java.awt.Color.BLACK);\n",
    "        penDown();\n",
    "        RandomTree.randomTree(length, minLength, thickness, minThickness, minAngle, maxAngle, minShrink, maxShrink);\n",
    "        display(drawing());\n",
    "    }\n",
    "    \n",
    "    \n",
    "     public static void main(String[] args) {\n",
    "        RandomTree.drawTree(20, 2, 12, 1, 10, 30, 0.75, 1.0);\n",
    "    }\n",
    "};\n",
    "RandomTree.main(new String[0]);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0df21288",
   "metadata": {},
   "source": [
    "#### Miniübungen\n",
    "\n",
    "Versuchen Sie folgendes herauszufinden\n",
    "* Was macht `random.nextDouble`?\n",
    "    * Was passiert, wenn Sie stattdessen jeweils 0.5 einsetzen?\n",
    "* Was ist das Abbruchkriterium?\n",
    "* Wie sieht ein Teilbaum aus?\n",
    "* Wieviele und welche rekursive Aufrufe werden jeweils gemacht?\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "c7651785",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6535088010433959"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import java.util.Random;\n",
    "new Random().nextDouble()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4f0724f4",
   "metadata": {},
   "outputs": [],
   "source": [
    "// Abbruch basiert auf Länge und Breite des Astes"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Java [conda env:ijava]",
   "language": "java",
   "name": "conda-env-ijava-java"
  },
  "language_info": {
   "codemirror_mode": "java",
   "file_extension": ".jshell",
   "mimetype": "text/x-java-source",
   "name": "Java",
   "pygments_lexer": "java",
   "version": "17.0.3-internal+0-adhoc..src"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}